Class 10th Mathematics AP Board Solution
Exercise 7.1- (2, 3) and (4, 1) Find the distance between the following pair of points…
- (-5, 7) and (-1, 3) Find the distance between the following pair of points…
- (-2, -3) and (3, 2) Find the distance between the following pair of points…
- (a, b) and (-a, -b) Find the distance between the following pair of points…
- Find the distance between the points (0, 0) and (36, 15).
- Verify whether the points (1, 5), (2, 3) and (-2, -1) are collinear or not.…
- Check whether (5, -2), (6, 4) and (7, 2) are the vertices of an isosceles…
- In a class room, 4 friends are seated at the points A, B, C and D as shown in…
- Show that the following points form an equilateral triangle A(a, 0), B(-a, 0), c…
- Prove that the point (-7, -3), (5, 10), (15, 8) and (3,-5) taken in order are…
- Show that the points (-4, -7), (-1, 2), (8, 5) and (5, -4) taken in order are…
- (-1, -2), (1, 0), (-1, 2), (-3, 0) Name the type of quadrilateral formed, if…
- (-3, 5), (3, 1), (1, -3), (-1,-4) Name the type of quadrilateral formed, if…
- (4, 5), (7, 6), (4, 3), (1, 2) Name the type of quadrilateral formed, if any,…
- Find the point on the x-axis which is equidistant from (2, -5) and (-2, 9).…
- If the distance between two points (x, 7) and (1, 15) is 10, find the value of…
- Find the value of y for which the distance between the points P(2, -3) and…
- Find the radius of the circle whose centre is (3, 2) and passes through (-5,…
- Can you draw a triangle with vertices (1, 5), (5, 8) and (13, 14)? Give reason.…
- Find a relation between x and y such that the point (x, y) is equidistant from…
Exercise 7.2- Find the coordinates of the point which divides the line segment joining the…
- Find the coordinates of the points of trisection of the line segment joining…
- Find the ratio in which the line segment joining the points (-3, 10) and (6, -8)…
- If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken…
- Find the coordinates of point A, where AB is the diameter of a circle whose…
- If A and B are (-2, -2) and (2, -4) respectively. Find the coordinates of P such…
- Find the coordinates of points which divide the line segment joining A(-4, 0)…
- Find the coordinates of the points which divides the line segment joining A(-2,…
- Find the coordinates of the point which divides the line segment joining the…
- (-1, 3), (6, -3) and (-3, 6) Find the coordinates of centroid of the triangle…
- (6, 2), (0, 0) and (4, -7) Find the coordinates of centroid of the triangle…
- (1, -1), (0, 6) and (-3, 0) Find the coordinates of centroid of the triangle…
Exercise 7.3- (2, 3) (-1, 0), (2, -4) Find the area of the triangle whose vertices are…
- (-5, -1), (3, -5), (5, 2) Find the area of the triangle whose vertices are…
- (0, 0) (3, 0) and (0, 2) Find the area of the triangle whose vertices are…
- (7, -2) (5, 1) (3, K) Find the value of ‘K’ for which the points are collinear.…
- (8, 1), (k, -4), (2, -5) Find the value of ‘K’ for which the points are…
- (K, K) (2, 3) and (4, -1). Find the value of ‘K’ for which the points are…
- Find the area of the triangle formed by joining the mid-points of the sides of…
- Find the area of the quadrilateral whose vertices, taken in order, are (-4, -2),…
- Find the area of the triangle formed by the points (8, -5), (-2, -7) and (5, 1)…
Exercise 7.4- (4, -8) and (5, -2) Find the slope of the line passing the two given points…
- (0, 0) and (root 3 , 3) Find the slope of the line passing the two given points…
- (2a, 3b) and (a, -b) Find the slope of the line passing the two given points…
- (a, 0) and (0, b) Find the slope of the line passing the two given points…
- A(-1.4, -3.7), B(-2.4, 1.3) Find the slope of the line passing the two given…
- A(3, -2), B(-6, -2) Find the slope of the line passing the two given points…
- a (- 3 1/2 , 3) , b (- 7 , 2 1/2) Find the slope of the line passing the two…
- A(0, 4), B(4, 0) Find the slope of the line passing the two given points…
- (2, 3) and (4, 1) Find the distance between the following pair of points…
- (-5, 7) and (-1, 3) Find the distance between the following pair of points…
- (-2, -3) and (3, 2) Find the distance between the following pair of points…
- (a, b) and (-a, -b) Find the distance between the following pair of points…
- Find the distance between the points (0, 0) and (36, 15).
- Verify whether the points (1, 5), (2, 3) and (-2, -1) are collinear or not.…
- Check whether (5, -2), (6, 4) and (7, 2) are the vertices of an isosceles…
- In a class room, 4 friends are seated at the points A, B, C and D as shown in…
- Show that the following points form an equilateral triangle A(a, 0), B(-a, 0), c…
- Prove that the point (-7, -3), (5, 10), (15, 8) and (3,-5) taken in order are…
- Show that the points (-4, -7), (-1, 2), (8, 5) and (5, -4) taken in order are…
- (-1, -2), (1, 0), (-1, 2), (-3, 0) Name the type of quadrilateral formed, if…
- (-3, 5), (3, 1), (1, -3), (-1,-4) Name the type of quadrilateral formed, if…
- (4, 5), (7, 6), (4, 3), (1, 2) Name the type of quadrilateral formed, if any,…
- Find the point on the x-axis which is equidistant from (2, -5) and (-2, 9).…
- If the distance between two points (x, 7) and (1, 15) is 10, find the value of…
- Find the value of y for which the distance between the points P(2, -3) and…
- Find the radius of the circle whose centre is (3, 2) and passes through (-5,…
- Can you draw a triangle with vertices (1, 5), (5, 8) and (13, 14)? Give reason.…
- Find a relation between x and y such that the point (x, y) is equidistant from…
- Find the coordinates of the point which divides the line segment joining the…
- Find the coordinates of the points of trisection of the line segment joining…
- Find the ratio in which the line segment joining the points (-3, 10) and (6, -8)…
- If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken…
- Find the coordinates of point A, where AB is the diameter of a circle whose…
- If A and B are (-2, -2) and (2, -4) respectively. Find the coordinates of P such…
- Find the coordinates of points which divide the line segment joining A(-4, 0)…
- Find the coordinates of the points which divides the line segment joining A(-2,…
- Find the coordinates of the point which divides the line segment joining the…
- (-1, 3), (6, -3) and (-3, 6) Find the coordinates of centroid of the triangle…
- (6, 2), (0, 0) and (4, -7) Find the coordinates of centroid of the triangle…
- (1, -1), (0, 6) and (-3, 0) Find the coordinates of centroid of the triangle…
- (2, 3) (-1, 0), (2, -4) Find the area of the triangle whose vertices are…
- (-5, -1), (3, -5), (5, 2) Find the area of the triangle whose vertices are…
- (0, 0) (3, 0) and (0, 2) Find the area of the triangle whose vertices are…
- (7, -2) (5, 1) (3, K) Find the value of ‘K’ for which the points are collinear.…
- (8, 1), (k, -4), (2, -5) Find the value of ‘K’ for which the points are…
- (K, K) (2, 3) and (4, -1). Find the value of ‘K’ for which the points are…
- Find the area of the triangle formed by joining the mid-points of the sides of…
- Find the area of the quadrilateral whose vertices, taken in order, are (-4, -2),…
- Find the area of the triangle formed by the points (8, -5), (-2, -7) and (5, 1)…
- (4, -8) and (5, -2) Find the slope of the line passing the two given points…
- (0, 0) and (root 3 , 3) Find the slope of the line passing the two given points…
- (2a, 3b) and (a, -b) Find the slope of the line passing the two given points…
- (a, 0) and (0, b) Find the slope of the line passing the two given points…
- A(-1.4, -3.7), B(-2.4, 1.3) Find the slope of the line passing the two given…
- A(3, -2), B(-6, -2) Find the slope of the line passing the two given points…
- a (- 3 1/2 , 3) , b (- 7 , 2 1/2) Find the slope of the line passing the two…
- A(0, 4), B(4, 0) Find the slope of the line passing the two given points…
Exercise 7.1
Question 1.Find the distance between the following pair of points
(2, 3) and (4, 1)
Answer:(x1,y1) = (2,3) and (x2,y2) = (4,1)
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d =
units
Question 2.Find the distance between the following pair of points
(-5, 7) and (-1, 3)
Answer:(x1,y1) = (-5,7) and (x2,y2) = (-1,3)
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= ![](data:image/png;base64,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)
d = ![](data:image/png;base64,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)
Question 3.Find the distance between the following pair of points
(-2, -3) and (3, 2)
Answer:(x1,y1) = (-2,-3) and (x2,y2) = (3,2)
d = ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
d = ![](data:image/png;base64,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)
Question 4.Find the distance between the following pair of points
(a, b) and (-a, -b)
Answer:(x1,y1) = (a,b) and (x2,y2) = (-a,-b)
d = ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
d = ![](data:image/png;base64,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)
Question 5.Find the distance between the points (0, 0) and (36, 15).
Answer:let (x1,y1) = (0,0) and (x2,y2) = (36,15)
D = ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
d = ![](data:image/png;base64,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)
Question 6.Verify whether the points (1, 5), (2, 3) and (-2, -1) are collinear or not.
Answer:let A = (1,5) B = (2,3) and c = (-2,-1)
⇒ AB = ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
AB = ![](data:image/png;base64,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)
⇒ BC = ![](data:image/png;base64,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)
BC = ![](data:image/png;base64,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)
⇒ AC = ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
AC = ![](data:image/png;base64,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)
⇒ AB + BC is not equal to AC.
∴ Points are not collinear
Question 7.Check whether (5, -2), (6, 4) and (7, 2) are the vertices of an isosceles triangle.
Answer:let A = (5,-2) B = (6,4) and c = (7,2)
⇒ AB = ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
AB = ![](data:image/png;base64,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)
⇒ BC = ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
BC = ![](data:image/png;base64,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)
⇒ AC = ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
AC = ![](data:image/png;base64,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)
As all the sides are unequal the triangle is not isosceles.
Question 8.In a class room, 4 friends are seated at the points A, B, C and D as shown in Figure. Jarina and Phani walk into the class and after observing for a few minutes Jarina asks Phani “Don’t you notice that ABCD is a square?” Phani disagrees.
Using distance formula, find which of them is correct. Why?
![](data:image/png;base64,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)
Answer:let A = (3,4) B = (6,7) and C = (9,4) D = (6,1)
⇒ AB = ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
AB = ![](data:image/png;base64,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)
⇒ BC = ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
BC = ![](data:image/png;base64,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)
⇒ CD = ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
CD = ![](data:image/png;base64,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)
⇒ AD = ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
AD = ![](data:image/png;base64,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)
As all the sides are equal the ABCD is a square. Jarina is correct.
Question 9.Show that the following points form an equilateral triangle A(a, 0), B(-a, 0), ![](data:image/png;base64,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)
Answer:let A = (a,0) B = (-a,0) and ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGgAAAAYCAMAAAAh4EhSAAAAAXNSR0IArs4c6QAAAJlQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OjoAOjo6OjqQOmaQOma2OpC2OpDbZgAAZgBmZjoAZjo6ZjqQZmY6ZpC2ZrbbZrb/kDoAkDo6kDpmkGY6kLbbkNv/tmYAtmY6tpA6tpBmttv/tv//25A627Zm27aQ29u229v/2/+22////7Zm/9uQ/9u2/9vb//+2///b1H4HIwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAB1klEQVRIS+1V2VaDQAxlcMPaRVwrigWXaa3AyPz/x5lkZsJSqHCOfdI8tDAhN7k3IXjev/0pBaSo7JDE9ePqkPAVdnmb/Voi/Tp97wXLz7pccvbmjjfXQvizIdXoaIGP6ViIKYczevIArvVEiJOGhMUFnKNJscj0iz9AXx1dYoCOTjMVHbWp6Sc4SfxnT0VNsOKcsIsAGQ9qZG7Ac8TJha2TCRVTYJsgmGz55CnqIIdwITQdmSYkmK8M2x2RRJcfIBHndE+U9K4GXGProgiIBCqHiahMsq8t/qZWfBVj+6GqTCeGBEleD+CK+L1rsCXJXCKTDk3FAsmVV6RrGQrBg2VLI0G7EvVQ6kn0sSUtq+HeBG5QOBEUNUI6aeKddFWPigCkkdVw5ALu9eYmEHYqEmRvdayzSPZK54YBwKxhsfWxxcTYI5hok50SUfpB422lM9PbGG+4oeE2bScfPVzvEfj8pTfohXVh2FbSz807qrkmggC2ghcWfMhK3RlGZWicKWh5fP/zCmJcBTsLJ4sPgOTEiKRiAJsjVgr/nyE1ya6GnhnrOLabgT1l6AagDHc2Ui3ebIYRZncdR6RLvpSdm9u4RxNCrWh7jzPe3mPC9n6PuoHs9+gbE7cv4lSAhcIAAAAASUVORK5CYII=)
⇒ AB = ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
AB = 2a
⇒ BC = ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
BC = 2a
⇒ AC = ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
AC = 2a
As all the sides are equal the triangle is Equilateral.
Question 10.Prove that the point (-7, -3), (5, 10), (15, 8) and (3,-5) taken in order are the corners of a parallelogram. And find its area.
Answer:let A = (-7,-3) B = (5,10) and C = (15,8) D = (3,-5)
Let these points be a parallelogram.
So midpoints of AC and DB should be same.
⇒ To find midpoint of AC and DB
![](data:image/png;base64,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)
⇒ For AC = ![](data:image/png;base64,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)
AC = ![](data:image/png;base64,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)
AC = ![](data:image/png;base64,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)
⇒ For DB
DB = ![](data:image/png;base64,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)
DB = ![](data:image/png;base64,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)
DB = ![](data:image/png;base64,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)
As midpoints of AC and DB are same the points form a parallelogram.
Let us divide the parallelogram into 2 triangle ΔABD and ΔBCD
Area of both triangles
⇒ Area ΔABD = ![](data:image/png;base64,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)
= 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PcG23ez9sy0h7D05Ncyr6yBBFZTtiTXHevId9oOhlFeD/vZThgvMlV50lBf/kd5M1DJmsv04h3T/5PnE0GJilFIiARkAj8PhBokbf4W4iCuHHyLS+JgERAIiAR8DUCgrwz8LiX2oib/38TKe5+/3uIvkZWKicRkAhIBMaIgJltsoPiAPz9PLMdAS92SVZ4fZK8JAISAYmARMCPCPwPDeUo+ge626sAAAAASUVORK5CYII=)
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= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= 77
⇒ Area ΔBCD = ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADQAAAAeCAMAAABUkc2JAAAAAXNSR0IArs4c6QAAAIRQTFRFAAAAAAAAAAA6AABmADo6ADpmAGaQAGa2OgAAOgA6OjpmOjqQOmZmOmaQOma2OpDbZgAAZgA6ZjoAZjo6ZmZmZpDbZrbbZrb/kDoAkDo6kGY6kLbbkNv/tmYAtmY6ttv/tv//25A625Bm27Zm27aQ29u22////7Zm/9uQ/9u2//+2///bqp8/TQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABC0lEQVQ4T9WT1xaCMAyGUydOhgsHah0U2vd/P9MhwkEL9cJzzA09NF/G3wTghyaOQ+dsl2nkDgHQ/4BE7Dcq8vQRySBVzu+hy6EcyfhQgqZSFNBtoRwzT151DETVoRbY/Mgj0j1raPNKknk2KJudaB3iwdKaCR+uDiU+c4bYJG0NjT3Sl+3z8ABlSAqEVlHPlCe2a8hjrEophBDdfFSv6ElJl3k+MBOZtIV4YMa5ZU+JfHKZSVkjpKcgwU8ea/mxZpvkYienp7cCyBd4mJ1MIj1Qn8bIOukGukeEzC1TXo2hIR7u4ap7cNknVGhU2RlrfcUlbd7YWqCrbsnJ6BcMQ4aVVrRNQh7IaXSDHucrHKJWN8sUAAAAAElFTkSuQmCC)
= 77
Total area of parallelogram = Sum of Area of triangles
= ΔBCD + ΔABD
= 154 units
Question 11.Show that the points (-4, -7), (-1, 2), (8, 5) and (5, -4) taken in order are the vertices of a rhombus.
(Hint: Area of rhombus
product of its diagonals)
Answer:Let the points be
A(-4, -7), B(-1, 2), C(8, 5) and D(5, -4)
Length of diagonals
AC = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMYAAAAaCAMAAADbudM7AAAAAXNSR0IArs4c6QAAAI1QTFRFAAAA///b//+22///tv///9u2/9uQ29u2ttv/kNv//7Zm27aQ27ZmkLbbZrb/Zrbb25Bm25A6tpBmZpDbOpDbOpC2tmY6tmYAZmZmOma2OmaQkDpmkDo6AGa2kDoAZjo6OjqQZjoAOjpmOjo6OjoAADqQADpmZgBmZgA6ZgAAOgA6OgAAAABmAAA6AAAAKzIlAQAAAAF0Uk5TAEDm2GYAAAIhSURBVHja7VfbUsIwEF1KqSZiMVqtKAW8oNaS/P/nObmX0tJNZcaRIQ90oJM9e3bPXgA4n/M5n77DxL89NRajBTmFZCTr8SnQoIVOyu06HqrKp8uwC8OxuqHyVFle3g9PSvKmbMDFixBzBIsa1g05DlT0GSvLmfo2fReC3wVEhys3km/5iL6uYcpJPwuFlVSySDkJ6EKbcSeULg26jbVXM4CpyNCxqYwptjHx1Sh1n9M9FWuspErR0VKKMRfaoVimwArwj3yD1FdUPhoaziTLoIeGAQmioU0b+q1QD8SbtDQKbJAyamg4Uc6hj4Z1P5RGVGbdULo0rDdUSFFxZNnR9dheNNTZHHpp2CuhNNghKN1unTdXFbbqZJkRf1EJkc4BaIqm8VqJD3Sjslpsh2JpTXaQVJlsC+Z17oa+Qd75QSWXcqItSNtRKV9523v36xKH0WIGk2Wb5dYfqDPcAmU2EROh0VIS1Z/9krI46aG20J0NHzdcHTqAHajJKvWbiDEdlbrEt+gZ26iNYBoGEdPaHd86FHt6URLbaX4mD+iG632ybQRBw5Z2noVkw4e2AaXEpjcRVz9M3I9Dxp9rH82ph5gbOScwWSITX/O9ASVDP3qOdyarWkY+rvFrpa1A1pXA7ik+WQkhsEtlTYlNKMaJW9LtTBm6G34HbHi/w9qDisrCz/OjbLhoHsOxWqAYfyNH+A/w1/83onIbwwkcVvxzAj/oMV7nwYuUWgAAAABJRU5ErkJggg==)
AC = ![](data:image/png;base64,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)
AC = ![](data:image/png;base64,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)
BD = ![](data:image/png;base64,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)
BD = ![](data:image/png;base64,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)
BD = ![](data:image/png;base64,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)
⇒ Area of Rhombus = 1/2 × Product of diagonals
=
= ![](data:image/png;base64,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)
= 72 units
⇒ Area of triangles
Area ΔABD = ![](data:image/png;base64,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)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAYYAAAAeCAYAAAAowrl/AAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAA6xSURBVHhe7V09bBtHFn67cq/UYbqQBPTT6gBRSncnnqgUKSIFJxdMgBPlKiQP1hW2QJm03EQ5k3Jl0QFsFqEROcEpACWer5WoAEcXKmQJIpnu0kcG3B13780sl3/an9nlLknZM4AKm7Mzb7739r2Z9zN7I5lMAm8cAY4AR4AjwBFQEbjBoeAIcAQ4AhwBjkA7Ak3DkEgsy8XVMIRgHZKessBh4ghwBDgCHIH3EwFqGJZHf5NnVrdg8vQYYPL9BIKvmiPAEeAIcAQUBKhhyF96hKAHDcR4QM6ecWg4AhwBjgBH4H1GgMcY3mfu87VzBDgCHAENBLhh4GLBEeAIcAQ4Ah0IWDIMJEC9PeOD3aUqBC/z1y5ATQPs21uwuTsO66UolFOpa7cGFvldHn0ph8+WYH0N15h/N9fIggPvwxHgCLAhkEjcrD+a9Ym7n19AyXMy0pWVtIGjVGA5kZDzNpVmP5WvFQXYMmoHkCvNg931scE82F75y6BQWgN5JjwDk+sl2VMePuMwrHJCONdP2gYrKdZnX/7gpRR+vSSQTce8F8RUKiVbH6V/T2BijbS/8FiIeoUrtCKfpeL2t8KD3TG4cxSFkDD867GD3M3Rl/Xw2aJ453YU3p4II+fnKclsnEZW0ktZEIhRIC0GvmwMApmqbPVU4KbyJUbAFwPIVEtw2dgFsyrA7pNOPlVu4kJ+qxX3YWszBllMyqItEIFMbqc5jxmIg/xdCxdCTyp/KZRyS/KMbwbGqyVZxWyQtKpzuyUny1Oj8tbmLoznWjJC5mSVE9UoKKdiZzcQenwaBn6oNBCl748eC5qaPpCBCipPr5AQS7VH9dnwjLC3fiRlEwkxOQTGIbE8Ks3640JJ7qR+AwKQDl1FmRiF7Vm/sLtYgGelEPjAvlFA3kr+OOKmBVwgTXHzCVcNkxO8J+tA/SV8+yAO2ZIMlITACqSf7YCnYQS+vwyOHP1dQJ59Ik7cOaz/cSxhahwaWUlBIZkMdtJ5mbdEt5HytTSQRmdkOio4orUDV35lUoDFLYgdR+Cg5EX3UecQxVUfhLIAkYMqJMt5IbE8Ja/6QhBDSTmQd+RhdjcZ4aIah1wGZF94G6ql3k6BRFmercvQ6+nDDTmhPAvjy033NshnL0DL9Cv8ZpETN2ijxsZAfnt9N5x8vvb6GFYOJMjOC01ln1j+ABVuVJi4+zX4cUfdMALiUe4L/P9ZIXNxJMV6MA6qgj67W++Y1+66IvtIf6hFPxnnzfP70P7at4zCBRxHfeLzHg1b9QxxI/N24KYYqom77hkFsrZixAcL3wH8tVABKeQT4dfi/275FsS/+QEK9Z36mIhGIJWSUt9fjhzlFuuzvk/EsYvD+hgYGwdLMQZDZhkoX7tMVnZw+NILIZiMROA4e6o5FHnp9RSg+rKj5tePKeBvHjQKigIpC2sZTNuNZWGviFa3F+JdfJYFFzK9d2EJArFd2K9FXaTGwtAOywlVulsVWM/JsLY/A+RUqdeM5IQ+4zBtrPJrAT1Xu/7HkxQ95fu4QWpNUzv4AY7lCNyZF2CHvB+Nn1L538VnGZD8Xz4ScEcs+dA4DLtbqbkq5HP8eAUKh14s6G2tyS64ZS3c9ncBzQXiZndUC8+t7MMTNAofKQZuZC09Xc/Gn4h7/3oMf3rbCqMS45BLy3XfV9vixWG0DoJiNLRmcsQwMClfC+ts71pcDcFppgol/xZkcWev13QVYG0fdvGwEVlHDpW795H4X56kkOzaX3r9pMpP9SvZJNzlx1hxQcsAS4EY7O7XoOtM6DKFV4d3Q06Isic1OBhkB9+ocpI2anpy4gZt1NYwyq8Z3YP4HTcf0qp4T5jOPIMFEU8Lyc54gjf0BW46foCD2td4whbgOty6pp4WYKWAa8KTRdeanMCZ4HaL4PYQcUMXkpuutvJHSfEevELrhn+N9jHqLwF+0VzKx5/iRjH+gm4UPSf6q3XEMICJ8rULdmIKK7JfZiC3g76Boukbr60Aq2eo4gOwhK6hy6t2QXPQ4h6xQBH4TNuW2F2OY89ZwSWVygtTkyAfn2Em2aCPPy7JiSVg9QylC7RZ4ZOlNfSpc+3RJjyRp9FH70WXC07a5YYFbwgWyabjoIahSXzBroNlQD6/wD3fCm7ls+1HIAcxrW1vQham4eGCF0oasDk4la7+kvG08tmfBXgrdhHw8aeoJ+N0o4jZR7osc8Yw2FC+ZuAorpKXsFTdoRlEiSnj3aBTClDxB5OYw85QprNaxaWJ8ylmm+3YjzOY8YvpdxfkhGnetk66cuIwbbb5ZHVBLvVXdtb3BDlSgJhfe2eNWIpTE7L0y1kV/RX40gxBO31wCwILWYmGmzCJJP3sMTnNtNxclM/T8DmSS46X3bau1yUQ3B4hbuREEsd53/QYv7BKT+LmKMYRBHGl8Bje/nQ1AymV+n4EeVY/Pq+KRn7yGxsbG7rHb7yS25E8/6nfNmQS4DVvAZp1FPXWgAQ7iQvJo5GHTzI8tvwl7UBolwKsVUhcYhL8GgHJbnqa7gQyr0GKp9X1aGUE2RlDpc8WLubgN3t004YyovyG+XzY2uRF4ZdTGU92MLGwrM6uFgylVbp6kV9Lc1VKZKN+xVXxh982pPksehNMG/JPZwwSb4kfyxBh2VmfVqEigeTDjCWzOAOuT1pA2lQhaskW2dqCotBpw2yiylGnUjdaD54EFwMv4OzObQw+74iYaljf/nJBiPvx/a8cSQnGGEg3ffpT6tBX/AYTXTAYTHAzMDxT/0UcvkMcTJ2f7DgoRglTBB5eQPbtTyOe83P9tFSU/8rjaP1EQOOhEWe44YTyN1O+1I/PeMxEJQOALiQCLhz7iKefQtdMpkVfZgz/jfFipqbEC06hgqddo6Yq3djkASRNivcsr0djYltj0OCoM7gYYdFNm4qNVlYS5Rdjc1xOGOdl6WZEm2Ve9SC/luZ6ntJ0BZAgMvP7pjMGdadOZ+B2V9CZBUsT2RLvtekCo6yk7mwio3HJ6QXm5sDz6jkkicsd008Tz9LSC8wMeoFukzhaUDJtO5+1xiOB5Hb6jObUoq/4zyeIWxrWTILONDZwjw1NFhxUoxCbKICMBWpJI6PAMK0jriRW5ctAD+2SKnvQkHRaEuKvFUKnrR1qd94p6+A6/UjaKjEK1R1S/MYYjOhxTquP94TLpH/gRX1Oy4lV/Iz6O0lbT3xyclE2x1JSVEGYxgIAv0bQ2eaw/X/M66eXRe+cVwEEJQbSzueQw94vpZZCwKDzAqb2uht07gaTpK3GJvbh4nEITvCsiKeAnvB2xDD0RIHTD3crQN84HkqzgLFXXZcaLT7CIHe1rSKaBg4ra9fy6o92SBVfNx7MMxai707zZBjHGwJDOYywEJqKW1Gaolr4Gmt8MOhsqmMmfQM3IMQFtDleEUhdQjMLqFZBXwHK/hh6HtwIKHQxsLgVoymqhagzabCs8kEL7P6dFi4O54lRoK4h1F/12cptsfShzukB5d//44+6JwtnDAOD8mVdpF4/5Qio33QVYCMLJbZXxA8QXX1eDTZnqtHmjppeiYAnCBhf65Vs1583wwXPzvhyYFYWZkhYrFl0nvY+yImZ21BXTlymzZRPzqNta0QlRRV3vZnbmimqXZsOpW+aunwH3n6JfYkZVErBHTRiDMdyl6KmfH4CbYcIR+hWUlTJaWHN9RTVDh40TikPL5RCOlKsR+49Kt7CYrex21fWhnTWb40I4vQ/CM9OdNfujGEwUb69Iq+4kRTRi+EVDxjwvHrFg44CJFkoifWIHAvtwZRGJbNi5Uk4oxVYVQNieAvAUDcWXGqk0CawBDkMvlurZXdh6S7ICY1/4JcHd/E+k/Y4FAQCcmQpB57ueJGeoXSBNhVBFj65gLa9IYt7qDYNUlTbR61V4TX2XdJLZ7VHga2n5tcOIPJ6E+Lo+4pjEJsMEoikofA01nkHEg1SxyH+M+a/L2B5G2Ps05QoxG0QKarFbxT9VWpbd1N/pTWo/hU3inIAFnGjGDvxwblOXpYjhsFM+ZqCatKh22erFfA0VIDza5AJ+GBzG11DXXMZBvsGvsU2BsYMF63TkB1eEP5CMEkytew83nzGDTmhtHmCSB7+dVOnwT89OXGDNpUcMz71BKrDDyOtGBT1wCVeI2GmM2lV9PQSPPUKoFXmwEKaEjS+h7LVWXHN8mx7H7yxQPxwLghJ/Gu1N/AKg+ut0i/iFsuLibsrUnzhZ2FfmpdCDJlULLSouLEEilnGY+1jGMR+8xyCbzpH+rVANoqLyDMAtAu6+brKJXp418wW3jWjXiIXwJSfoNXvPhsoX9ZF2u1npgDpS1+qyqBcjibnou/27aoER4pJeBcmD5xLJ7XLn47nhlhOYIC0OYJtHwdRA9Tpi447lPpIQQ9TIZ/TAT88eITusqiSrfQ+NLXGgbidTn40vmX1huJz3YTxxiVyy+i28YU2sbDM2o2cg1K+rApQpc+P32MIz+DdOnip3DBfkNeLoJJg+swWfo8Bbxkdtu8xDLOcDIq2Xng9iGepUQj/IEzsK3UGbl754Mb66KnhCCsvSM4/FKS/JBI93a7qBo1Oj0mNQviFOFE4bN66ajTHjVSqLHjwGH5ZVjzQXhqc0bmsruFSwOu4Ncfst/K1qgCp2wFzk4LBS1LV7DT2QzMeuWY66ME1Wqgx6Cfxwywn/aatn7g7MRe5mhs3HQLZdJDvMXj6XNnrxBrIGKpx8OP3GL6aqZLvMTAXwTlFQ7/GId9jmP0Gv8fw9FD3ewykIpq49ObQ/TSH7qcrMQbig8WPEdiuZu2n8h12Bdgvxl/HeYZZTvpJ23XjXf73oKhuOoaz2ocdURrfgA9hDjeKr+53xiLYRxn+nuR7DHMeEm+5z0xsh2EgbqTw3jrGF67fZzuZV8w7cgQ4AhwBjoAhAk3DQD+TSY1CmeGOFY4qR4AjwBHgCLyrCFDDQKt824wC+fcqfpaj1691vaug8XVxBDgCHIF3GYFGVtIGFklkOy6sI9dO88YR4AhwBDgC7x8C/wdEr7NNuwXziAAAAABJRU5ErkJggg==)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= 36
⇒ Are
a ΔBCD = ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= 36
Sum of area of triangles = 36 + 36 = 72 units
Thus proved
Question 12.Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer.
(-1, -2), (1, 0), (-1, 2), (-3, 0)
Answer:Let A(-1, -2), B(1, 0), C(-1, 2) and D(-3, 0)
AB = ![](data:image/png;base64,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)
AB = ![](data:image/png;base64,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)
AB = ![](data:image/png;base64,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)
AB = ![](data:image/png;base64,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)
BC = ![](data:image/png;base64,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)
BC = ![](data:image/png;base64,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)
BC = ![](data:image/png;base64,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)
BC = ![](data:image/png;base64,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)
CD = ![](data:image/png;base64,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)
CD = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIgAAAAaCAMAAABbyuQoAAAAAXNSR0IArs4c6QAAAH5QTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6Ojo6OjqQOmaQOma2OpC2OpDbZgAAZgA6ZgBmZjoAZjo6ZrbbZrb/kDoAkDo6kDpmkLbbkNv/tmYAtmY6tpBmttv/tv//25A627Zm27aQ29u22////7Zm/9uQ/9u2//+2///bvJa0jgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAB0klEQVRIS+1Va1PDIBBMoo22VaNVoxYfVEsa/v8ftBwXAtwxoY7jY6b3pdOE7O3uPSiKYxwd+IcOyPL3wrdLP6z/hnvdYmuI6JfFW4KQXL7+BFVVA4/2Eviw0c3v4fnHqiwvMjjliKJYwiTR7RVJoN/3eU+hbt25+emvn4pNNV1IRtSIhaIoVn9jKqJOaF1EeVfsGvtCztAvS8kL3Vq3xuBEeVgjQogFLaJbqE8YwjyTJeRx38jYOUqEFeVhOVEhFvzrzmJZAydliQwqN6RFCBFWFMAh1iAqwno2Vqtk5QXWDOwpJG1VQiQtCrFQVISFLZIi4lCFaRK156Ei7wiRpKgRy4iKsezwykG327GW2dh3hkjfmNceEREdtwVAUfHLCSwJuAkVXrnBES6II4Oo6PAEFu73BBFRu+y2R5jILY2PFYja3RovcL/zDQZzpmBe+4YuPMsqk4iHVQSi5HIFaaxQduRgzLQABmSPOW/ypsbHikXBVMN+N03CblboRSDilhApTt4ewc5lRel2ttWPuNm5tezlTBvCdA0nyj9GRMlqjS0Cxcm4fRP9SuYj1U9wkIrqm9rb9jlXdx6Rw0XJaj59p2cmD44dKqrHO/4rub7rm0/fLiw1FSbXgQAAAABJRU5ErkJggg==)
CD = ![](data:image/png;base64,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)
AD = ![](data:image/png;base64,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)
AD = ![](data:image/png;base64,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)
AD = ![](data:image/png;base64,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)
As all sides are equal the quadrilateral is a square
Question 13.Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer.
(-3, 5), (3, 1), (1, -3), (-1,-4)
Answer:Let A(-3, 5), B(3, 1), C(1, -3) and D(-1,-4)
Let us see the points on coordinate axes.
![](data:image/png;base64,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)
Let us first calculate the length of the sides,
We know that distance between two points A(x1, y1) and B(x2, y2) is given by,
![](data:image/png;base64,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)
Therefore,
![](data:image/png;base64,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)
Now calculating BC,
![](data:image/png;base64,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)
Calculating CD,
![](data:image/png;base64,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)
Calculating DA,
![](data:image/png;base64,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)
From the lengths we can see that, none of the sides are equal.
Hence, the quadrilateral formed is of no specific type.
Question 14.Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer.
(4, 5), (7, 6), (4, 3), (1, 2)
Answer:Let A(4, 5), B(7, 6), C(4, 3) and D(1, 2)
If ABCD is parallelogram
Midpoint of diagonals AC and BD
⇒ For AC = ![](data:image/png;base64,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)
X(4,4)
⇒ For BD = ![](data:image/png;base64,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)
X(4,4)
As the midpoints are same the diagonals bisect each other
Thus, the points form a parallelogram
Question 15.Find the point on the x-axis which is equidistant from (2, -5) and (-2, 9).
Answer:Let P(x,0) be the point
A(2,-5) and B(-2,9)
⇒ PA = ![](data:image/png;base64,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)
⇒ PB = ![](data:image/png;base64,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)
PA = PB
PA2 = PB2
(x-2)2 + (-5)2 = (x + 2)2 + 92
x2-4x + 4 + 25 = x2 + 4x + 4 + 81
8x = -56
X = 7
Point is (-7,0)
Question 16.If the distance between two points (x, 7) and (1, 15) is 10, find the value of x.
Answer:7 or -5
Let A(x,7) and B(1,15)
be the point
⇒ AB = ![](data:image/png;base64,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)
AB = 10
AB2 = 102
⇒ (1-x)2 + 82 = 102
⇒ x2-2x + 1 + 64 = 100
⇒ x2-2x-35 = 0
⇒ (x-7)(x + 5) = 0
⇒ X = 7 or x = -5
Question 17.Find the value of y for which the distance between the points P(2, -3) and Q(10, y) is 10 units.
Answer:3 or -9
Let P(2,-3) and Q(10,y)
be the point
⇒ PQ = ![](data:image/png;base64,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)
⇒ PQ = 10
PQ2 = 102
⇒ (y + 3)2 + 82 = 102
y2 + 6y + 9 + 64 = 100
y2 + 6y-27 = 0
⇒ (y + 9)(y-3) = 0
⇒ y = 9 or y = -3
Question 18.Find the radius of the circle whose centre is (3, 2) and passes through (-5, 6).
Answer:Let P be center such that P(3,2) and Q be point on circumference Q(-5,6)
PQ = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALkAAAAaCAMAAADc+w0uAAAAAXNSR0IArs4c6QAAAJBQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OjoAOjo6OjpmOjqQOmaQOma2OpC2OpDbZgAAZgA6ZgBmZjoAZjo6ZrbbZrb/kDoAkDo6kDpmkGY6kLaQkLbbkNv/tmYAtmY6tpBmttv/tv//25A625Bm27Zm27aQ29u229v/2////7Zm/9uQ/9u2//+2///b8Q0ZPwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACb0lEQVRYR+1Wa1fjIBAN1ZXVtdru+ojrVnxguxoS/v+/k5kBQgLk4QePPTof9DQH7ty5zKsovu1bga+lgGT7ZMHb6Ju7PX0pdfq6p8yrIySuH06f3hmBXD7OuznH1wC4uEbi5fn7pH82uaZOEKP4f8HY2XgQ83xlwZs/ILUuV8h/e8zY4cS8VxwqewGn1U/42/zeFFv8PWjWF7i75z8yeumdUYGY5MApzasDTBWx2BR1Oe4cmSlOSoNJx4DctKbL9pD9an0Zp/zsJRejYFdFvSZWGXC5guBLSnYB/ySLnCXxQ+aeMMINMne+DPGrHO8ukwz4Pb52IF8hKNJRCy+5DNj20zzW3F1r1qTWgFWkYRqc0rxqE6S+ndopuuEiDRnVZ8zc+bK0hpg7DTEV+uDUEz3zZs3YcmKTUfwX9+UsINErQ7zqplqeuTj4B61owJmXJgku0ZEMEmTH3Q/htwL7JN0P+sYUkStnAIewWVAk0X3U1/rSJTN9eMdX+DF1tO1BKXA7+oNsMaoxQptkyrnOtLes5rrEGyhn0nwl9w/Vl6C2Hf0d5o7MJOauzigVYxtjHr5297Y48jF1wOXyAjOTHNqMoveZUDr0wnDYhtmsM++U7y1UflnNsYlXiNoHR4I0+l0/15C1NT3juAk8TEXRH0D+dszcZYHiRtRtbnYgoEZxInBINP3Xtm471+pbM9GHyj2Mp7409WhbqB9z/YAHZqiC+b7JKGRLFplH4HJx5zfcto7HtU6cyEqeQpvrKwY3xdXO6nn7W4+QW+cmRj3PVwpcLk7a9WjOztxj+PH7eWN3sYlSfaZjcnTn+Uxsicsb7ag+u8vB4gAAAAAASUVORK5CYII=)
PQ = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAG0AAAAaCAMAAACKASIdAAAAAXNSR0IArs4c6QAAAIdQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OjoAOjo6OjqQOmaQOma2OpC2OpDbZgAAZgA6ZgBmZjoAZjo6ZmZmZpDbZrbbZrb/kDoAkDo6kDpmkLbbkNv/tmYAtmY6tpBmttv/tv//25A627Zm27aQ29u22////7Zm/9uQ/9u2//+2///bOxnO6QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAB00lEQVRIS+1VaVPCMBBt6oFSlCJeVahHUFKb///7zB5JSpKWOozMOGM+AFP27cvu233Nsv/z1zsgxS+fboP00/qI/WqK7RHZ1DmS6dfi3bPK2dvPrjAWXj8iWXW9U2IzxcfZ51KIq/3EY+HtDZSkqzmm3FwKkd/Dr+YC5GwXq2yT7xXWwg1CUnQPnGRTJ9hGmT8YRoHM8oyLJaA/uqKyO4fhwDLhu6XhElLrCsXjrxp5HAlGDLIxDnpR3jFbGv4CF28mLB6S1kzNzQ1li2tjOEDnitmcNl04yWZDlIBOcjyRymhGYjYLz1Sxdb9TcJp/F/IxMVPCMmFDlSFTuzr1s7WLtU+VgkvMJGlITEdN96Sg7BDeluBqnq12JtcdVIZj88zFKWcCzrbFtekKyqFPCk+d3tqUvYpjc/CvW3jGtsVsbUlTQpVS4+MzoFtXlC5czpYoC2V0M4nlUFFtGUy+5R2aST8CAVyBHGRbdtGMZMa/eLvDpXZFxmx+35yX+HUlHMijn9mJrRmAc52u8H9nBmEvB73EaEfzE8KNo7m3TcfoOHlvaWkpw65HcDMT3pT6TDw9KNHTEXCZT73fjn1B9dDvh7clL/XIAg4Mkz0bdWDaCP4Nge4xd7/eRWcAAAAASUVORK5CYII=)
PQ = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAYCAMAAACsjQ8GAAAAAXNSR0IArs4c6QAAAH5QTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOjoAOjqQOmaQOpC2OpDbZgAAZgBmZjoAZjqQZpDbZrbbZrb/kDoAkDo6kDpmkGY6kLbbkNv/tmYAtmY6ttv/tv//25A627Zm27aQ29u229v/2////7Zm/9uQ/9u2/9vb//+2///bDQpfXwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAA5ElEQVQ4T81RSxaCMAxsUARU/IGiqEUpYLn/BU1SCl3wwKVZ5MEwycwEIf6qJIzVYLE936b96oOaJlSrmcB5goQiBPCOxGwzgOjhzLSXpxDSOyEJtvg99VWTLhCzVUcKUZbJfSUqDy1XQFu7kjxmCNhzGtYxv39K6ncKWQFJ4DApEAF7kwHR9I7lXgGaRKohcH+XvM2ErAMUkqjsECxKdgbYSvBYi2nMnTtTtLIziQvZWkIh7QaOSTp9TNxXGKqEjTKHogBGx+BhdxE69fJKWLMHWNvfp2P3pv3tnAc59yfHhn7FvnunEu01NIovAAAAAElFTkSuQmCC)
PQ = ![](data:image/png;base64,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)
PQ = ![](data:image/png;base64,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)
Question 19.Can you draw a triangle with vertices (1, 5), (5, 8) and (13, 14)? Give reason.
Answer:Let A(1, 5), B(5, 8) and C(13, 14)
⇒ AB = ![](data:image/png;base64,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)
AB = ![](data:image/png;base64,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)
AB = 5
⇒ BC = ![](data:image/png;base64,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)
BC = ![](data:image/png;base64,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)
BC = 10
⇒ AC = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAL8AAAAaCAMAAADR5X1pAAAAAXNSR0IArs4c6QAAAJNQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OjoAOjo6OjpmOjqQOmaQOma2OpC2OpDbZgAAZgA6ZgBmZjoAZjo6ZmZmZpDbZrbbZrb/kDoAkDo6kDpmkGY6kLbbkNv/tmYAtmY6tpBmttv/tv//25A625Bm27Zm27aQ29u22////7Zm/9uQ/9u2//+2///b/odcDwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACdElEQVRYR+1WaVPbMBC1QgtuaQIYktKaI+IQAXzo//86tLu60OGYjGeYzESfcuzqPb09i+JwDgocFAAFBNu/40VO3qz3Oo7t/H2v+TcnSF8+zp93eIdYPH3Na3Ic/h/p1+e7haE9Rf/ibcnY2fan7ITzojI8h9NfgeyyvtDYryssB7n5zdjPocrQhkX7C6z6y/tiM9taSREONpC8X1tCb8H/MziU/s0RJU+3ZPSJz+6Lrs5fbA0V/LGOHCF4R9YUG3ciHCBWDvF3N6RxBAgvayqCdvEkNH/4QbAQ3zBxhkYYMDcxNFYR/xhHRa76O46/lecTzgPGprRENX+kwHVUAhHpqzU0ObGJ0j/in8LhF804/kkcSn/vBse/uxvsLc6QY/BEXL0R/wROM38fyb9I4VD3TNzbV4wthlqSxx8KoFH0myDdRvDvL9c+ehjptvxT2jbCEzgCIb2k8T6+liZ/uN0wXKg/84fnMr9cUi4xDuaEUo9oFJGTvPnn2gjwD3D08pDMH3UxCyvS0yfQP1Uj2/VvjDC5RoFdpSQaqL853Qpc9PKQ4W8ch+tX52XCaDt/dBrIf/y/r6g7Uv7TEYslZpPum2H/oVpvsv0TbjDJ1Ve5KI3qP4P8OVytZQxwkBwtD7b/Ay3McAmjq6v9gIX62qkZjS1rme3/Foe0zPdPjjRIqQBHKnbyVu9sei7KO5jXP67VIIZPZ9n+4wy9+Ru+UKmQmb++u4oyLQip060UH93G7fw1KTRb293Z7SWZi/I/5+VP+EyJo8rCTeKd9kKMqt4/R757ShwxO3Vxm3wvzzxoQpy+GtpvRgr6nWbCa6jfyePr2B9ADEjG8xtmFwAAAABJRU5ErkJggg==)
AC = ![](data:image/png;base64,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)
AC = 15
Largest side is AC = 15 which is equal to Sum of other two sides AB and BC i.e. (10 + 5 = 15)
∴ triangle cannot be drawn infact the points are collinear
Question 20.Find a relation between x and y such that the point (x, y) is equidistant from the points (-2, 8) and (-3, -5)
Answer:Let P(x,y) be the point
A(-2,8) and B(-3,-5)
⇒ PA = ![](data:image/png;base64,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)
⇒ PB = ![](data:image/png;base64,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)
PA = PB
PA2 = PB2
(x + 2)2 + (8-y)2 = (x + 3)2 + (y + 5)2
x2 + 4x + 4 + 64 -16y + y2 = x2 + 6x + 9 + y2 + 10y + 25
-2x-26y = -34
⇒ X + 13y = 17
Find the distance between the following pair of points
(2, 3) and (4, 1)
Answer:
(x1,y1) = (2,3) and (x2,y2) = (4,1)
d =
=
=
=
d = units
Question 2.
Find the distance between the following pair of points
(-5, 7) and (-1, 3)
Answer:
(x1,y1) = (-5,7) and (x2,y2) = (-1,3)
d =
=
=
=
d =
Question 3.
Find the distance between the following pair of points
(-2, -3) and (3, 2)
Answer:
(x1,y1) = (-2,-3) and (x2,y2) = (3,2)
d =
=
=
d =
Question 4.
Find the distance between the following pair of points
(a, b) and (-a, -b)
Answer:
(x1,y1) = (a,b) and (x2,y2) = (-a,-b)
d =
=
=
d =
Question 5.
Find the distance between the points (0, 0) and (36, 15).
Answer:
let (x1,y1) = (0,0) and (x2,y2) = (36,15)
D =
=
=
=
d =
Question 6.
Verify whether the points (1, 5), (2, 3) and (-2, -1) are collinear or not.
Answer:
let A = (1,5) B = (2,3) and c = (-2,-1)
⇒ AB =
=
AB =
⇒ BC =
BC =
⇒ AC =
=
AC =
⇒ AB + BC is not equal to AC.
∴ Points are not collinear
Question 7.
Check whether (5, -2), (6, 4) and (7, 2) are the vertices of an isosceles triangle.
Answer:
let A = (5,-2) B = (6,4) and c = (7,2)
⇒ AB =
=
AB =
⇒ BC =
=
BC =
⇒ AC =
=
AC =
As all the sides are unequal the triangle is not isosceles.
Question 8.
In a class room, 4 friends are seated at the points A, B, C and D as shown in Figure. Jarina and Phani walk into the class and after observing for a few minutes Jarina asks Phani “Don’t you notice that ABCD is a square?” Phani disagrees.
Using distance formula, find which of them is correct. Why?
Answer:
let A = (3,4) B = (6,7) and C = (9,4) D = (6,1)
⇒ AB =
=
AB =
⇒ BC =
=
BC =
⇒ CD =
=
CD =
⇒ AD =
=
AD =
As all the sides are equal the ABCD is a square. Jarina is correct.
Question 9.
Show that the following points form an equilateral triangle A(a, 0), B(-a, 0),
Answer:
let A = (a,0) B = (-a,0) and
⇒ AB =
=
AB = 2a
⇒ BC =
=
=
BC = 2a
⇒ AC =
=
=
AC = 2a
As all the sides are equal the triangle is Equilateral.
Question 10.
Prove that the point (-7, -3), (5, 10), (15, 8) and (3,-5) taken in order are the corners of a parallelogram. And find its area.
Answer:
let A = (-7,-3) B = (5,10) and C = (15,8) D = (3,-5)
Let these points be a parallelogram.
So midpoints of AC and DB should be same.
⇒ To find midpoint of AC and DB
⇒ For AC =
AC =
AC =
⇒ For DB
DB =
DB =
DB =
As midpoints of AC and DB are same the points form a parallelogram.
Let us divide the parallelogram into 2 triangle ΔABD and ΔBCD
Area of both triangles
⇒ Area ΔABD =
=
=
=
=
= 77
⇒ Area ΔBCD =
=
=
=
= 77
Total area of parallelogram = Sum of Area of triangles
= ΔBCD + ΔABD
= 154 units
Question 11.
Show that the points (-4, -7), (-1, 2), (8, 5) and (5, -4) taken in order are the vertices of a rhombus.
(Hint: Area of rhombus product of its diagonals)
Answer:
Let the points be
A(-4, -7), B(-1, 2), C(8, 5) and D(5, -4)
Length of diagonals
AC =
AC =
AC =
BD =
BD =
BD =
⇒ Area of Rhombus = 1/2 × Product of diagonals
= =
= 72 units
⇒ Area of triangles
Area ΔABD =
=
=
=
= 36
⇒ Are
a ΔBCD =
=
=
=
= 36
Sum of area of triangles = 36 + 36 = 72 units
Thus proved
Question 12.
Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer.
(-1, -2), (1, 0), (-1, 2), (-3, 0)
Answer:
Let A(-1, -2), B(1, 0), C(-1, 2) and D(-3, 0)
AB =
AB =
AB =
AB =
BC =
BC =
BC =
BC =
CD =
CD =
CD =
AD =
AD =
AD =
As all sides are equal the quadrilateral is a square
Question 13.
Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer.
(-3, 5), (3, 1), (1, -3), (-1,-4)
Answer:
Let A(-3, 5), B(3, 1), C(1, -3) and D(-1,-4)
Let us see the points on coordinate axes.Let us first calculate the length of the sides,
We know that distance between two points A(x1, y1) and B(x2, y2) is given by,
Therefore,
Now calculating BC,
Calculating CD,
Calculating DA,
From the lengths we can see that, none of the sides are equal.
Hence, the quadrilateral formed is of no specific type.
Question 14.
Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer.
(4, 5), (7, 6), (4, 3), (1, 2)
Answer:
Let A(4, 5), B(7, 6), C(4, 3) and D(1, 2)
If ABCD is parallelogram
Midpoint of diagonals AC and BD
⇒ For AC =
X(4,4)
⇒ For BD =
X(4,4)
As the midpoints are same the diagonals bisect each other
Thus, the points form a parallelogram
Question 15.
Find the point on the x-axis which is equidistant from (2, -5) and (-2, 9).
Answer:
Let P(x,0) be the point
A(2,-5) and B(-2,9)
⇒ PA =
⇒ PB =
PA = PB
PA2 = PB2
(x-2)2 + (-5)2 = (x + 2)2 + 92
x2-4x + 4 + 25 = x2 + 4x + 4 + 81
8x = -56
X = 7
Point is (-7,0)
Question 16.
If the distance between two points (x, 7) and (1, 15) is 10, find the value of x.
Answer:
7 or -5
Let A(x,7) and B(1,15)
be the point
⇒ AB =
AB = 10
AB2 = 102
⇒ (1-x)2 + 82 = 102
⇒ x2-2x + 1 + 64 = 100
⇒ x2-2x-35 = 0
⇒ (x-7)(x + 5) = 0
⇒ X = 7 or x = -5
Question 17.
Find the value of y for which the distance between the points P(2, -3) and Q(10, y) is 10 units.
Answer:
3 or -9
Let P(2,-3) and Q(10,y)
be the point
⇒ PQ =
⇒ PQ = 10
PQ2 = 102
⇒ (y + 3)2 + 82 = 102
y2 + 6y + 9 + 64 = 100
y2 + 6y-27 = 0
⇒ (y + 9)(y-3) = 0
⇒ y = 9 or y = -3
Question 18.
Find the radius of the circle whose centre is (3, 2) and passes through (-5, 6).
Answer:
Let P be center such that P(3,2) and Q be point on circumference Q(-5,6)
PQ =
PQ =
PQ =
PQ =
PQ =
Question 19.
Can you draw a triangle with vertices (1, 5), (5, 8) and (13, 14)? Give reason.
Answer:
Let A(1, 5), B(5, 8) and C(13, 14)
⇒ AB =
AB =
AB = 5
⇒ BC =
BC =
BC = 10
⇒ AC =
AC =
AC = 15
Largest side is AC = 15 which is equal to Sum of other two sides AB and BC i.e. (10 + 5 = 15)
∴ triangle cannot be drawn infact the points are collinear
Question 20.
Find a relation between x and y such that the point (x, y) is equidistant from the points (-2, 8) and (-3, -5)
Answer:
Let P(x,y) be the point
A(-2,8) and B(-3,-5)
⇒ PA =
⇒ PB =
PA = PB
PA2 = PB2
(x + 2)2 + (8-y)2 = (x + 3)2 + (y + 5)2
x2 + 4x + 4 + 64 -16y + y2 = x2 + 6x + 9 + y2 + 10y + 25
-2x-26y = -34
⇒ X + 13y = 17
Exercise 7.2
Question 1.Find the coordinates of the point which divides the line segment joining the points (-1,7) and (4, -3) in the ratio 2 : 3.
Answer:Let P(x,y) be the point
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)
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)
![](data:image/png;base64,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)
P(x,y) = (1,3)
Question 2.Find the coordinates of the points of trisection of the line segment joining (4,-1) and (-2, -3).
Answer:![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/4RDuRXhpZgAATU0AKgAAAAgABAE7AAIAAAAMAAAISodpAAQAAAABAAAIVpydAAEAAAAYAAAQzuocAAcAAAgMAAAAPgAAAAAc6gAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAGFobWFkIGF2YWlzAAAFkAMAAgAAABQAABCkkAQAAgAAABQAABC4kpEAAgAAAAM5MwAAkpIAAgAAAAM5MwAA6hwABwAACAwAAAiYAAAAABzqAAAACAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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)
points A(4, -1) and B(-2, -3) are shown in the graph above
Now points of trisection means the points which divides the line in three parts. From the figure it is clear that, there will be 2 points which will do that. Let us call them P and Q.
Now clearly point P divides the BA in the ratio 1:2 and point Q divides the line in the ratio 2:1
⇒ Let P and Q be points of trisection
∴ P divides BA internally in ratio 1:2
Such that AP = PQ = QB
Let us apply section formula to the points A and B such that P divides BA in the ratio 1:2
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUQAAAArCAYAAAAAP/H9AAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAABLzSURBVHhe7V09bBtHm35nkV6uP7ZcAierlQGTqs2P5AHnrwgDsKEak04TLoGoiRlKpOVKh0hKcyJT2GpknJpzgFCKrz1RASJ3p+hgkl/pPkqv3XtmhksuKf4subvSSt6t7NHuzLzPDN95/+eLSqVCwRMgECAQIBAgQPRFAEKAQIBAgECAgEQgYIjBTpgZgXI5Y+zGVLooGRQ6q7KZOwg+8C0CWFt9dyXCLl5cUT3BlEq1avh2sh5MLGCIHoAadBkgECBwNxEIGOINrFt5+ZPBknUxUu7IoLVWnrJanU7x/2juiOKhM5ZZ+GQMt9mZ2vKndaPbNTrboXazQLQbI1Xjvcvx/CjFeYkJp/smcPGSBimFR0g77QpoWNsW1lbt7FIsopFsjtJOq0maSr6R5ICJrqTqzMD8cg2d1tpf06pWo6bY6w06rSeV9m7+arVQZ9a2SmW6JGpKr8WmQZL8bWqdaKT+c5dWIkVq8kGByXbrBJgwpTqHdBswRDtcx+E71bMQM9o7RkzV6HwzT439GsUvQ2x/4b2hakm+U4yF0hrFK2bbJqXbTePyYLo6ehaqsKMcZ4r4cewX6KBaZeXyvrFz6G+V1ktM+HLdBC5e0lCtHrBys6WD+zGN8MPnzJBIqR5cGs2jnK4kztm2z5ghxx2YKHprV1+JFNj5q+fUeLNHzcKe0v4xdhUppFg0mtMb6hqYV63b9orttBK6ppanMnVgopRPgAlU+qLxA33kzJBJTE4az8CIz9kPH+dnhnz+AUN0yOxm/XypVCOT0YVTaYpySS69RpdnB8IWJ9s0umgThWx2nqi1aedcJS27CwmxbHQgIR6m2xS/I/Y9LzDh0N0kLl7QwBlA5qvHerFwwToQfiLYITwmpNM6h/hVIi0CG1+l4lsb39KLPSGpcTtkOPOV2OtG+lvSkmHM22wriL3Oub2dR2DyJTAp/h9rQ05USZqwBSbPSlQEJn/ZkDbHjRUwRDur4PE7S5EwRJr5BxHSxP6OcQgJNJs/REclqOGSwbrxDKif6HB9fV12mxRDWH6QkFLbzR7DdzK2U0z42F7jMo0+N2gIJ7+ix1qB3v26J/AuG3B6xN6z7f0EaTVAX61Om8bEvz/6tK4n6l2uMrC2Cv9O7640/snVcyl9OXG0LKlhqe47mLYQGopF+vl4j1JQsAzhCPpvtv3671SoOYMkYIiOtpN/PobawPZ3olDBCUwpAabkgMMOkcXVT2u46iQvM6Rf/4DCf3ce4nIjhIaTlH6skfbuV34CEf2aoyKl6SPOUFiLnfAVMf3fQxVIa31KJnmZL9++FBLqrT/hFH0ZLVLx52MSHPFoi4rGl8DEuQwQMMRbX117E+BM6DifxU+iRBU4YYa/KpeXjXzsE+VydZzieToyasYZ7Inme5nMsrGVTVJd+lp6zhx7o/vvLbv0TMNlGq5eUz5t/L7a/I41dEM/fq5AM7zi6rNQO/n8MplH+lY2waxry50Xflanx+GKddW3VlOsDseJ3KfSEWN1uvTV5p+BSUI//vqnPiYWRwpn7sfPV1nK+I6MoT7GjR8wRK93vAv9cw90LL9FS+fgZkvXO5QSW5YW95tUCD8lqicpmX8KxinfFUyBbdLiUZsqsFVm4PVWk/YdNy6Q4GoXdumZhss0XF2d9IjO7I4f/uZ7eqYlaPPHReyBZ/S0xqjeVTvL5Ud6XnnJFhswxME21z7OX0USm3BUGHBU+Mf7bAdLrKv+XNlki798JCOpKh1OS+oVnEfS6WL1GocLJcoVU/Rq919o6X+ByX8QQVvuSczAVl/Jb7GH500yRvxmAoZoZ0W8fKd9IcJsRq3NeatzzYFibTuARzoO5pZZjBr1i8FJSglDlU4UeKW5wlo7yuFATNL7nbYRvzxg1eoZC1Xi3HEjPg6ri7AIwQh928+cmNihxw4uk3C1Dc2cNPD+7Y5frf6u/OMZ6XVNYzDkUd0iHfK/hTbk2nLVNxx+SI/ZLa9t+w+x1x+OAPG83SFi8KBYdG+zrVo5U/7GafnwlqofcJBn5D4dpQhjDyj/9szQ68UiQ5wNMBm0bQJb5Yn8zeg/XRCz63kKJETbO3/+F8uZBYTcSPN0HYZxxAYaNRXxZDD4CQ0WR/nSmLZJMYSmLU+GHGZFqE4hfEx5Jsc6Rb8wKAqmaJ19pwHHy86+K86PeVFxE5NheubFZVZa3KRh2th//0eOGEJZS9+olJxgPOwc/SfR9j480H2Velrfbv69nHmAkJt1EYdYTyk8FlH/PrOASJkCQm34Xo/Itsj1tvXkYOiNWNftN8KRczkipjDxNEf0E9GLQphbVx3bUzkOczNEcQLvbtHm4SKVECNltVe5CbDZVwYxe9mLNJXWMJaN+Dwv5jBvn9ywH8fxHTc7OKsiXosQdzi9bdKY3IuKTgjCn3i4Q4NLiCH02zuAL6VU2MMR6nL2nTMvtDkumPW8kAhnhx36R+E0jZ55cJmHELdosD127ikllfGhNplHn/Tsf5XYaV2d237I7XP0ZAPB/HCgzOGXqx78qTzZqNATk6gPL+klpD07bRW8Z9mn+uq7EmtyWi4nBG0/e0opgcn0wG47OM/FEM0T+DB9RPvNhAgGtjOYk3cOLuOsuUZGLBujpVLT8GP2hUnfTR8WdnEVh4pghtedMnb78NN7940eK7am/RM/MNiFO0g+ykLwq40Ntck8eN9lhnfTmTJwyC287zLDxACjkx7wVUav/4cK6j8J/6bt13szh9pg3+irF2n23bcFSsLOarVNfjGoXgxud0SVUwmLYJXI+swQNiuoYgf8CL+hh5/Izf001M8YLdrM5LihqfWG8eqwkDYxrgq3KFMuG7MeQjzNLGZhhvz/eZih/XywTFo7t+hxiqvT/TV5/N/ocAuhJVAItaUjBC+Plg7LkAxjQjKUzJD/P2/UGHxrrklOTum0+z1P/VsRkqFkhvz/z2mP1VBookywP8LIdPjvHJN/peLDX8hAIPblGOlQepk3IKy1qKUndZVJxwyEK+VkjfSV1Rj7+bsTvV7uq+pfyBShI+OCISQDebVmSEdmecHIJjXOQQdDOI63kF+Zo6NmGGqyXTLde0/GlZGhdrMyZmUM7s3kek9eHRZcEmJduyCMMKTWNaQtX7cNjqNNemXXsZVE/rSwL3PWmjvifrm797hFj1NcnSJnZ3wwOSwUctRrCQojEBs/6IFhpZc5wU4NkSuv86B5ubYI5B7pjnA6a+++l17mDdbs0dLdpw1OS//5rZ4Cgdv0cS9J6phAbC4FKoq0ZRIiNyP1IlKfW/ppl/mBjygnb9Kwd66wnY8negHtnFl2VWaVFqODhB6cmYG+dXp3DEkCfzZ/8EDbc5vhJNhletshNTrcuuyjx6PDgpsLKqah0CR3yDY4CQXplbXYFc2Xb+NEc2G53KLHKa5OSZk0vrSDbnTtw5fcLDVyOOllHrW2sAH6IoraPkrcc/y3DdA8/AnskNy+CASEfXNDGCj/orcvx0tkXArcgMd64PnrLcUtn3Cm+Gab9Mjqjyx5UtDLYIoTbYjhCA8SOaVeCEinQYcQMXKlBFLNBlXleauLXFPZuxVbwryqh+mF5WlD1pQwRKqnoxodNjp9R4V93D150y+HhSfEBZ0GCNxTBGQa4CEddb6BXZJN9jKLhGk8vZxMEXMVpTTU6Msh0+G81UWkyt42wP2gDMryVaYajKoeKJt1fi0/ln+zvETGKbLCeXyeL54Jh4Uv5hdMIkAgQOA6At00wMOjDmkFdTxDlDZEiIOQ2NYgENpJjZ23ughncJl01NC0C+KFL8zHrOoxtgzWORwMtdkcDMOFCsbvkRkLFUw4LIJ9GCAQIOBPBHiY0fJDQ//tos14wPigygwDLgyyXaN7VOS7cmOuKbFJiXGJxhVncVJdxCx7NWivfI/4YW8LFUxaJrcKFcDQbTdQ3p+75jOcFby1U0PJgnW9kxtjdIwmhCvuiR5kiBYvsyT1DMywrxtLm+I5IdNs7DN3dZGuXVB7dyxzcLmDAlU92qjqMRha7M9FmHRY2Plx+ZOqYFaTEAjW9f7tj7kCsyfBMK26yLhv+2rzO1pGpZbjPFLccInRxLCapcjMQeFeqcx2Dov7t30CigIE7hcCszFEURSgPraa87TqItOgExUsUFJ/c5dX9cihqsc1Z7boQsahcfPmCO/OlEGGa/vdhMo8je7g7wECAQK3jACEq4hCZthNmy7GlWKxznNYrbX8zU51kV6IDaLuR9X04/FlyNc2UNWDFyWg0LiUwE4Liju83akw8ndvGUhz+CmHhU9mGUxjRgSm7dkZuwte9xkCMhicscc/qKKSdy91T8S5c6dKdMewhr5Y5y+cJqWcoSWlWmsWdLBbXaRsAwxRwYJX9UAFi3Fxw7wKxmk0Tft+si9OOCxskB28EiAQIHAbCAjh6rEQrvgtgCJ1z1oxBRGGY6PixXwTa7QTVaHW4pa4LgH2q4ssG1wSHRXYPYAFqnqMq54jSy5xAbIfr3gbOA6POe6w8MPcgjk4QUBqT1P3rJMhgm9vDQEhXD1O0+vu9QOz2RAxbWsgNardGPsF+9VujvObSIyGKmy5DW5UVY8dFJQYdSeIYIbZQ9QOdOciI9dXYcRh4foYPujQ1Agu4PS6q8Uh7MI4as/a/fYuvicrykTYxYsrqqOggpMLpfxOP/gJcpmJbX/8Rl5n2s9lnm3qJlOMoB5iNtZCPcTywP0d43o7C8VZqFu1efAdVLCwVPWojKh3yBPhY1uoh4hySH6th+jksJhtBYK3bwqB8Xv2pmYQjOMFAoIZrh6yh7/ImwTNArQzS4jm5ISajJIP8fglV28dz9la1WNUSTGeCB8PYSyf3eo2UnVGKuKsh8U0AHm5K5YUll5ecZvWWnnKaqJ6Te/CKH5Hx3DbtH5v4+/3iRan+E3Dgpf0au/mrrKFOjPX2s8XSPFyXUqqLqrMoDI2rbW/plWtJuxz5oVR7d381Srosba5VeDVznrwSjgrW6iH+Lop6iHCedtLnJibIdoZ2M47g/bHKfZLOx364B23DwtOUvUsxIz2DuynGp1v5qkBs0Icd63sQ3JWEaqE3WYslGDXrZht/r1E6j7R4nS7TcIignVFTVK9oa7h4KuBMcauIgV/XyAFehS9tQtVtMDOXz2nxps9ahb2lPaPfO4pZtLTNECPaHuFC7HkJVI3pZ7zSjhPIFx9eFslS5FusZS3zhCdbqjP8fulErexyirlMuURskN6jV80ZGnTxsaL+gmz+0SLU1yHsXhc5Ov6LWm4TY9LUOal9RcdCDS4h9QflySPp3rpxV7vYvtw5iuxTw0rPaKtIPYpwVHqhydgiH5YBRfm0KtI5EJfw10MZ/fwIqTiwYVZeCx52jMWxBgzVy9p8QAeT7vkWHSv0vZknEef1vVEvV9Jtr+2Ch9P7640/om1bUl7mxNJbkkFPd0rVD0hyGGnAUN0CODn8Plwds8kL7NbBTE+B1z9QOPvoQqkz/5MJnmZL9+iUKsfJu3hHAKG6CG4futaZhNlcUNHaWSmkN/mO24+mcyysZXFlRdd0YlXZbovF2fNswbi7pB8FpeAlHhyxdw37s0zttvfYG31rdUUq4s7S/uOmJtyugQM0e0V9Wl/3AMdy28hRxxchBctuqOPzGPfpEXEs1ZgM83A+64m/etA8hrmzANcMJXfYnd9XTlOMo1uky3+8pGMpKp0jvNXkdQrtt11ulhvx/MK14AheoWsF/2KIrSj+VnvmgfLuNa2A3ikeXXxzGLUqF94MbkZ+5yTFnmfSpw7kMSAYZFDLiu739lnChbDHge+rmbbwZ8hRazrw6j+0x/EfFF4s/2H2KcPRyzIeRtzRyFWq+5ttlUr/E4VrO2Ht1SF+7eckWs7tTCliwsfMEQXwfSyK5myKE3cdTgzEIto1FTLvTOaigye0W1+yyZxkxaeeoUqwj2vu5dr4EXf07GIYK11vawuUCxSkA4JTbatJxGq4tIF7W7RVs48QMiNvO2unlJ4LKL+fWaBEIZDQgvmc+dtkettgh5LTKBY2+03A4HTbs1zXD8BQ/QaYZf654V347B+9+4RQ+ULXrvXTptLU+h1Y8aOgtHO1bVbtHB1OSvumpbhRnfxsYfFS7nWuF2vv/7e3KrHS+rzm+1CZ+h/jivXqwd/Kk8wT3ExHn9wY95LSHt22vjNeuaDte1eVq8qlct+4LTXaxwwRK8RDvr3BAGeyimZ4dmdZYaeAHMPOuWZJKuWy+pvkqSAId4k2rc8lvQyc7Ubl3OVZ7uc65anPjA8T3eLWZgh/3+ecHe4pWiIn+br9Vykl3kD9kPcC2IYOix0olCB1+N60T9P/VuxMEP+/+e0x2o3VGgiYIherKoP++QSFWNmmK1Gal1DxfG2Eb+8W+qm9DKvw2gv8ri7F6Lx/G6UV/8Mn8yD97rCYLMTtGsUEeva0k/X/WdfnLY80su8wZqGyNnXefw/37G5xt60T137+/8DVUj4LB6YPAMAAAAASUVORK5CYII=)
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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
⇒ Q divides BA internally in ratio 2:1
![](data:image/png;base64,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)
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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIoAAAAoCAMAAAAWjZKzAAAAAXNSR0IArs4c6QAAAI1QTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OjoAOjo6OjqQOmY6OmaQOma2OpCQOpC2OpDbZgAAZjoAZjpmZmYAZpDbZrbbZrb/kDoAkDo6kGYAkGY6kLbbkNv/tmYAtmY6tpA6tpBmttv/tv//25A627Zm27aQ2////7Zm/9uQ/9u2//+2///b4N9ujgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACg0lEQVRYR+1X21YbMQy00xLccknLlhYMoW5pDdmL///zakuy403IWsuh4Af8kBNObJ0ZaTQSQryfmjJgJZzl5u1BmWuPoVPhs4pjP/ytAocQQ3NRCRJhFz8rgeL08VshMdg0/mA2WlmNaE0NnQx16VQ1ojXvnbzfKm2pk9396UEDtOd/XrH5nP46MZ+6E273TTHaoZMTfPwm5ccruOD0tKi7Tzx7JEZuLeVpMZNbgnZxJdxvCRjakqgtywqIkdPLTa9LIX1XE0HsbqeDiMpOzEsLMQJhciyVCJpowh4RrQ/eoJcbv9qgMJwOf3YK3LpUQXqBswWMY2jKgwYJOkpgp/yL2F8BntNRoiHP6TdTDhwZ4buhKdcUCcabAD5CCUHsVsCw4FhimgfenW/UGxQGoeBn4QDBEZS0VHXqbLV9HermbrB3OCPsAJQ0l8dfUtQnC+RzkFthUHNL3DhQiFEsEKOkGDXJ1ksjefFw+T3vQR8btuJwPQ88XaAoW8b8RSgtOgqoPS7gvhoj4Q/Nl0scB6xtNDKyoQc5zRwJGgkWF1iTrzjj0QWIyWcM4t260aQMI6OgQ6hSya8iQXevpDxCUYI3eSNZ+KxIeZFCJBdmuW161vuRcg5dNK2XzDg7RaLccbChIYW0FIpntnvzI8UJdN3D50SdkpsTbOXxpv8BJcon868wJL1wYidzJ/OuJ0OceMziTvQwZ+IZE3xQcgVOtD/dnV7dYlL4+8rUrgE9CIqmwyUI0gn1nndK+0q21/IJzoPAu92vX3UfPAwqNOf8PPNIzr/1qMoL1fyoz3tBHv+8xy/7qor/DNFzWJPpZdnvR4MtuufsU/8biRD92s889NPR+Qc50EBEMG7YsgAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
Hence, Points of trisection are
and ![](data:image/png;base64,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)
Question 3.Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6).
Answer:Let P and Q be line
∴ A divides PQ internally in ratio a:b
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
⇒ Given that A(-1,6)
6a-3b = -a-b , 10b-8a = 6a + 6b
7a = 2b, 14a = 4b
∴ a:b = 2:7
Question 4.If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.
Answer:Let A(1, 2), B(4, y), C(x, 6) and D(3, 5)
If ABCD is a parallelogram
AC and BD bisect each other
⇒ Midpoint of AC
![](data:image/png;base64,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)
⇒ For AB = ![](data:image/png;base64,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)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEAAAAAeCAMAAACrM+hrAAAAAXNSR0IArs4c6QAAAIdQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OjoAOjo6OjqQOmZmOmaQOma2OpC2OpDbZgAAZgA6ZjoAZmZmZpDbZrbbZrb/kDoAkLbbkLb/kNv/tmYAtmY6tpBmttv/tv//25A625Bm27Zm29u22////7Zm/7aQ/9uQ//+2///br5EmFwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABTklEQVRIS82U2VLDMAxFlQKlAQqlaVkCSQElxNj+/+/D8Zp1kJsX9NJJRzq+kq8M8I9CnjaL1FT3xwCQ+esZMJwA1Omq4Om6IeGmAMDWDe5o9eAAIkt0mC7w8pl0fJs6OYPq9u8G5Mf2C0CW115qGOLPu8yvPsca8CH8KfNHVYmt6r3N9IAq3cgy6WvAVaHS+J27KJm7MlqvXF1Mm8lv9A8Au1D66SGyJwMANMJkHmfAcs8swErgaZTp2LZxANu7+6Q1IQ4F+IpSa7efxjsz4eH6UFWBWnWph4AxM2TuhA4groWOZqdgCUDPgHgLnds2TgQQmXYg0QchTc2hb0WaE0U2sot1opIw3IXvY5LsBr44vQyN4ndBEdptDCEOb1DbPuftFbZRjUG/B70I+BlE9z2YSsG4FR8h6uEIaJvis3BhPVP1LGrJ+wLNs04E/AKQAhuxN+RvagAAAABJRU5ErkJggg==)
⇒ Midpoint of BD
For BD = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFQAAAAfCAMAAABOKhpcAAAAAXNSR0IArs4c6QAAAJBQTFRFAAAAAAAAAAA6AABmADo6ADqQAGaQAGa2OgAAOgA6OjoAOjo6OjqQOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjpmZpDbZrbbZrb/kDoAkDo6kDpmkGY6kGaQkLbbkNv/tmYAtmY6tpBmttv/tv//25A625Bm27Zm27aQ29uQ29u22////7Zm/9uQ/9u2//+2///bQOs/fQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABpklEQVRIS+1V21LCMBBNULSioiDW4oVWCai0NP//d27YJt2ElK4MvrkzzNDMydnb2Y0Q/9ZUoEqe9muxGsnBIzlWUsrBgl0zPR85Up01f/X8TawpiaKOHazTiUotkxAeuroikcVJc4i+lHIv03JMmCjp9iUN0h/bbwfbTu6FKODnWz1b6ix93cBpPYG6gaHfXJ5TUjhpau/B1HCjn5chqWmAlENDCual/xk0UGc2pBZWTxfKD1S/3xgnsfQBbCNDb3P6TW7kF7OlULcfbWXudgF+JWc2gRa9SjxJ6QIU5cpBSKvEBFpdW9W4bNjqiwChJ+bUKqV08R1PWixs66Fju0peHk9mb+bSygxDjQ7n8W5QGuUvJpnjKzeJN6So9w5ryfphuSmqOkGfaAY70pOn/yekpqbM7nOVV5t9xdUpl7QZKd5E1ZPIWxORGE4UhOrvLCG+H6SbEHuvCJYqnMdg7pXQGW4pa/U0eJfimo/B3JaCWHGfUvPepe5BCmBkn8buBGu8i5YJw+tr97YdHHcmDDkUj5MJQ84SOMt+BTFhyIlvby9pN+wH/OgkZpA1FhUAAAAASUVORK5CYII=)
= ![](data:image/png;base64,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)
∴ ![](data:image/png;base64,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)
1 + x = 7 , 8 = 5 + y
x = 6 y = 3
Question 5.Find the coordinates of point A, where AB is the diameter of a circle whose centre is (2, -3) and B is (1, 4).
Answer:Let O be the center O(2,-3)
⇒ A(x,y) B(1,4)
∴ O divides AB internally in ratio 1:1
![](data:image/png;base64,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)
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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
x + 1 = 4
x = 3
y + 4 = -6
y = -10
Question 6.If A and B are (-2, -2) and (2, -4) respectively. Find the coordinates of P such that and P
AB lies on the segment AB.
Answer:AP = 3/7AB
∴ P divides AB in ratio 3:4
![](data:image/png;base64,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)
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)
![](data:image/png;base64,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)
Question 7.Find the coordinates of points which divide the line segment joining A(-4, 0) and B(0, 6) into four equal parts.
Answer:![](data:image/png;base64,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)
⇒ Let x,y and z divide the line into 4 equal parts such that
AX = XY = YZ = ZB
⇒ X divides AB in ration 1:3
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUQAAAArCAYAAAAAP/H9AAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAABNLSURBVHhe7V09cBrZlj6Xci7HTylQtTKpXGVQbB6wVesXjKaKBCUGTzK0qkbJmEECy5G2RtIkK5jAViLXKllP1QiNN12jqRo5W422DLzQ+Whyde937qVFg/hpmm5Anu5Iarrvvec7l8O55/deqVQi//IR8BHwEfARILrng+Aj4CPgI+AjoBDwBaK/E8ZGoFhMG/uxEF0WDFo8L4uxB/BfmFsEwFt9fyUsLp9fUzUhAqVy2ZjbxXqwMF8gegCqP6SPgI/A3UTAF4hT4Ftx+ZMhklU5U7Zm0EYjRxmtSmf4P5qtUXzxXKQXPhm99+wsbfnTptEeGoPtUbOeJ9qPUUjj0dV886jFeYkJ0z0NXLykQWnhYdLO2goaeNsAb0OtfYqFNVK3o7TXqJMWornR5ICJHkhVhYH1ZU902mh+RWtahepyr5/QWTUZaO7nrtfyVWG9VyqN1kRN7XW9bpAif5ca7zUK/XOfVsLrVOdJgclu4z0wEYGyA+3WF4h2pM6Ez5TPF4XR3DNiIY0utnN0clih+NWiOFx4Z4S0JO8UY6GwQfGSeW+bVpt14+po9HH0fLEkalkWivhyHObpqFwWxeKhsXc830daLzFhdk0DFy9pKJePRLHe0CH9hEb44rMwJAqUj66Mei2rBxIXYnfOhCHjDkwCemNfXwnnxcXLZ3Ty+oDq+YNA84fYdTifEtFoVj8JbUB4Vdr3Xoq9RkLXQsWRQh2YBIrvgQmO9OvG9/SRhaFQmLw/eQpBfCG+/+hcGPL6fYE4obAb9/VIoUKmoAumVinKmtzqBl2dH0lbnLqn0WWTaNHm4IlKk/YuQqRl9qEhFo0WNMTj1SbF74h9zwtMGLpp4uIFDSwA0l8+0tfzl6IF5SeMHcIxIa3GBdSvAmlh2PhKpbm18UWeH0hNje2QwfSXcq8bq9+Qlgxi3ea9vNzrLO3tXBKTL4DJ+v+JJvTEECkTtsTkaYHWgcmfNrTNQXP5AtEOFzx+JhIOQqVxPonUJg73jGNooJncMQYq4BiuBKwbV9fxEwNubm6qYZNyCssXElpqs34j8CeZe1JMeG6vcRlFnxs0BJNf0iMtT29/OZB4Fw04PWLvxO5hgrQKoC+XRy1j6OcPP23qiWpbqnTxNsDv6W1O408+nivtaxJHSyQUVMf9CZYtlYb1dfrp9IBSOGAZ0hH032L31d8pX5kMEl8gTrSd5udlHBvE4V4UR3CCUEpAKE0gYXvI4uOnNVx1mJcZ2u/8gMLfOw9xmQqhwSStPtJIe/sL/wIR/ZKldVqlj/gNhbV4Erkil//bYgnaWoeSYV7mqzcvpIY68yuYoi+i67T+0ylJiVjboXXjC2AyuQ7gC8SZc9feAlgIneYy+EoUqAQnTO9bxeKykYt9omy2il/xHNWMinEOe6L5XDq9bOxkklRVvpYbZ4692efvKbv0jMJlFK5eUz5q/s6x+a040Q399FkAJ8NrPj7LYyevL51+qO9kEsLKW3ZezPNxehCu4Ku+s5YSVThO1D5Vjhir06VzbP4JmCT0069+7GBicaSwcD99tiZSxrdk9IwxaH5fIHq9410Ynz3QsdwORS4gzSK3B1QaW4aWDuuUDz4hqiYpmXsCwamelUJBbNNSrUkl2CrT8HqHkvYdNy6Q4OoQdukZhcsoXF1ddJ/B7M4f/Po7eqolaPuHJeyBp/SkIqjaPnYWiw/1XOCFWDqBIQ62ueZp7jqc2IajwoCjYn68z3awBF/1Z4FtsfTzRzKSoUCLaUm9hPNIOV2sXuNgvkDZ9RS93P8XivwvMPkPIpyWbzRmYKuv5HbEg4s6GX2+M75AtMMRL59pXsowm368uWi0bjlQrPeO4JGOQ7ill6JG9bJ7kUrDCCknCrzSfGCt1LL4QUzSu72mEb86EuXyuVgsxdlxI18OhpZgEYIRetaXQ0zs0GMHl2G42obGIQ08vt35y+XfAv94SnpV0wQMeVS1aIf82eKW4i0ffYPBB/RIzJi3zd/lXn/QB8SLZotIwINiOXub98ql88DfmJYPb6j8AT/kabVP+x2EsQcC//bU0Kvr6wJxNsCk27YJbAOP1XdG//GShF3Pk68h2t75zh8sphcQcqPM01UYxhEbaFRCiCeDwU+eYPFTHhlwb1gMoWnLUyGHGRmqkw+eUk6ouc4wLgyKUihaV986geNl79AV54dTVNzEpJcep7iMS4ubNIya++//yJJAKGvh6xAlhxgPW7X/JNo9hAe6c6QeNbabnxfT9xFysynjEKupAMci6t+lFxApk0eoDe/1sLoXvn1vM9kdeiP5uvtaOnKu+sQUJp5kiX4kep4PsnV1Ynsq4+ALRDd3w4Cx2LAfx8933Pz8vIx4LULc4eh7w5bHXlQMQlD+5MUODdYQFzHuzQ/wldIKzYuPy5m3k3mhzXkhrB2j5xYm/ehxgosTQtyiwfbc2SeUDAwOtUk//KRn/qsgzqohx/ZDts/R4y0E88OB4sAvVz76I/B4q0SPTaI+vKAX0Pbs3CvhOcs+1dfeFkSdabkaErT99AmlJCajA7vt4OxYIMojyf4ObR8vUQFBo1YDvp2Jx30mjSDmzOUqFTYwl42A5XHHd/P5aWNjd+0SQykMbztl7I4xT899bvRYsTXtnyTtwi0kH2Wg+FUGhtqk779rC8O76Uzp+tFeeNcWhokuQac84GuCXv0P5UP/JPxNu68Oxg61wb7R1y5Xxbff5CkJO6vVNnmPN5WZ5sWLMlO9rGlJZkoYZ0HwM+aR5Hi1Bn4lZHaE11+Uo6u4qG+QEcvEKFKoG/OYjuYlNsomxkfhBqWLRWNczJmfMYsw5P9zMEPPK46j9pNb9EyK66h1jvp8+Py/0vEOQktwINQiNQQv99cOi9AMY1IzVMKQ/88ZFQHfmmua0yg63PqcU/9WpGaohCH//4wORAWFJooE+yOMTMf/zpj8K60/+JkMBGJfDdAOlZd5C7KpQQ09qYeEcsxAlgTeb5C+shYTP337Xq8WO0f1eyxomrUIvI5VyL3mzReE05JqWTh7qEbNSkfodYQhjPiwTR3x2W9KFx9R6oersMfFaMlmatuUlian8Qob/tESbbsgjDAUqmrMq1u2wUG0Kq/sJraSzJ+W9mUWrdka++Xu3uUWPZPiOilyduaHkAOjkKOO72AQgdj4QndNq7zMCXFmyFx5nYPmFW8RyN3XHTHpqr17X3mZt0T9hpb2Pj1hWjrXr9UUCNyljwdJCg0IxGYtMBBQtkxC5Ga4uo7U54Z+1hZ+kCWB969XYe9cEXsf3+t53GdhKY/MwcQG7UURv6btUKEdv6YMxlnEs/VogKc7SDjH/XoQx2TvwBk0sgq0JSPUTlMbV1PydMUeYcM/WiXTUGgS0GMbHEaX8spa7Irmw7NgoAsMcIueSXGdlJRh8ys76FbbPnzFp7C+0ykvcz/ewgY4F1HU9lFiz/HftkBz7yuwQ7J9EQhI++aWNFD+SW9eDBZArAVuwWPddf35huKWV1govt4lPbz2g0i+z+tFCEUpEK0pThy/ZlRUvTt4Prtsg6YGhJ+fWzZDp9VFuj2CWEy7YkuQq3qYXlhOG7KkhKl832M6abG7bT6uYdjMxwr9VfgI+Aj0IqDSAI+p1voadknR8TJ3Upy2KYe3LmCzuFUcoHVCxzhzZQsJ5N52H5WdVhdRVT2aBqQfDoOqfJWp9aGqB8pmXdzOj0XqzmpUo+OTVsdzO2teD8Fm1kvz5/cR8BEYgEA7DfC41iItH+oOu5HR3yhHVa2qo/J5r31QBqFGaRXhbVd9TIdOq4uwUEyvRg1NuyQufGFeZlWP3jJY/PxyhIwzlMnggOVxrt5CBYPfHbNQwQhsxlmj/6yPgI/AdBDgMKPlB4b+62VTcMB4T9hNiJaiWMhZlbb3UZ9vzDVNUl3ELHv19hSeT8yrjqDvED88pFDBBTyulfE8rr2FCoaR6FahAhi67QbKj4m4/7hXCMBbOzJywuerV+h7Om7/GE3IEvZEdwnE1n4GKWA1qkWQC2txsHRpbEg+G1atynF1kfYxWHt7qnJw2UGBqh5NVPXoDi32FCzHg0ttdgA2dr5cjif2X5wZAj5fZwa9ZxPfCETpVc5EEGSdoERrj6II7bAWCOAVBMOciXtBSL0deI2qLjLoxc6x+S0tw9N9mkOKG5oYue1F9urIbAcbz7joD+wj4CPgCgJSIJoe0ggEEGecsHlQ1dZL0ifk2NoN3h1VXWTUik0b5vY+V/XIoqrHLd9N9xCR8NgCcxZH5lF0+5/7CPgIzBgByJJwgFTYDR+VpYcXzmOzruiNgyWJ2npN1NbjdDlZJaXat7y9neoiNyE28GD3q+nH8WXI1zZQ1YOLEtDigAwYFZjLEToDvDuzwHYINrNYjj+nOwiM2rPuzOKPMisEVDC4EI++D8lK3vcW3m0aIVkt5Ywy+6kbR8ppDt5mucoq8v1k6ItByKnkcJcbO1+bCrvVRYo2qJYVLLiqBypYDIwbbjVwcIe3OxVEQQMbg07jkV4b6DTm9OfwEfARmAwBKUseSVnCXQDvXcVRHt50J1ukS+/R0qykUixkDS2p7HxmQQf71UWWjcsBcYxdVKGqx7BiEVwW6Cy6Sodz5HCRHvY+2EzGLf/t2SPQJFt7dvYL9VfgAAEpSx6t0qt2+4Hxq93INL+Qo7Cc09w2+h908qV5/f2qeuyhqsegniAqpZBP1J0Abgc4ePPKBNh4syBvRjVPBJewOdu1L3uzEu9H7bdnvZ91djOoijJhcfn8mqooqDBJQ6nZUWFvZsgS5DKT2P34tWpnauYy23tdPWXNLEGIjnGYt1/t5nwxLhbbVZu750QFC0tVj9KA8l7KE36MlEJ3OruNQ7edZyfBxs74/jPTR2Dwnp3+WvwZ3UNACsO1Y/HgZ9VJ0CxAO76GaBGKYdRDzMQaCNUpdjU0crJsa1WPfhV0uDJIbAf1EFEfbp7rIZpC0U1spCaNcl0CFYn44hJtG40cZTRZveamYRT36Oi954QXXr/zOdEyKVajsOCSXs397HUmXxUmr+e5gRSX6wqkqrLKDCpj00bzK1rTKtI+ZzaMau7nrtdAj/WeWwVe7fCDK+Gs7KAe4qu6rIcI5+1N4oQjgWhqitxKPR6/YnufnXX0fabb/ji4qgdXBokvYq45a3PZjyhJkwvYWMfmcmxGcw/mAo0utnN0ArNCHL1WDmU9S5SIimaNhQKyi0rmvfltIvU50eJ447dfHIZFGHyNRrP6SWgDP3wVCMbYdTg/3w2kQE9Ab+zjKJoXFy+f0cnrA6rnDwLNH3jtKWHSUzdAj7z3Eg2xVBOpaR3PuRLOY8iSD2/KZCnSLTniWCBOuhH8950jECmwjVUV5VUpj9AdVje40ZDlntY3PMr5rN68+TnRMilCvVg8Wme+fkMauumxBmU2rb9sQaFBH9L5aJI8mOrI84ObxvbB9JdynxpWeuS9vNynBL/APFy+QJwHLriwhsiwfMoJx+/N7uEipPJCwyxcljztMQtiDFiXl7RMCMXUX2cs2q20PZn74adNPVHtVJLt8DbA8+ltTuNP8Lah7G2TaHKREOhpt1D1hKAJB/UF4oQA/hVe7w3BGuZldqsgxl8B13mg8bfFErTPzkqGeZmv3qBQ6zws2sM1+ALRQ3DnbWiVTZRBh45C30yheVvvoPWk08vGTgaJA23VKYqCxZ9L4ywnPJC9Q3IZwXxFn1vHHfeczO32O+CtvrOWElXZs7TjiJmW08UXiG5zdE7HYw90LLeDHHFIEa7RcUcvlba5TUuIZy3BZsptSEPJ+XUgeQ1z+j4aTOV2xF3nK+Ok0ui2xdLPH9HMKRRoneauw6mXYrftdLF2x/MKV18geoWsF+PKIrT95dkFShD11sq13juCR5qL6aaXokb10ovFjTmmQ1pUP5U4O5DkhEGZQ86l1+7wNQKLXo8D89W8d/THYkDy9UFU//F3EnNReLP5u9ynD/qw5KKJtaMQq/Xsbd4rl7inCnj74Q2V4f4tphVvRxamdJH1vkB0EUwvh1IZOsrEXYUzA7GIRiVk6TujyR44fe/NWzaJm7Rw6hWqCN943b3kgRdjj8YiDF7rejG0QLFwXjkkNHVvM4lQFZcatLtFWzF9HyE3qttdNRXgWET9u/QCIQyH5CmY1873wrfvSXosMYGSt7uvuwKn3VrnoHF8geg1wi6Nz4V347B+31QxR+UL7vBg555LS7gZxowdhaB1NLRbtPBxOSN7Tatwo7t42cPiheI1uut1+O9NVz0uqc+d7RbPMb6DDsPloz8Cj7FO2RiPL3TMewFtz8497qxnXuBtu1l9KFC66gROe81jXyB6jbA/vicIcOaSEobnd1YYegLMZzAoZ5KsWZrVT5MkXyBOE+0Zz6W8zHzsRi+a4ni9aGa89K7pOd0tZhGG/H+O0IvnXAWr/9Uu5WXegv0QfUEMQ4eFThYquIs4cOrfikUY8v/P6EBUplRowheId3HXOFgza1RCmGG2GoXQIiK61zTiV3fruKm8zJsw2ss8bvmlZ6qyNZRX/wte6fvv9ICAzU7SrlFY8rWhn23On31xFHuUl3lL1A2Zs69z/L/k7cnBqFdd+/z/ASGgPv+4/acgAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
⇒ Y divides AB in ratio 1:1
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Y(-2,3)
⇒ Z divides AB in ratio 3:1
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUMAAAArCAYAAADi4+qEAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAABLgSURBVHhe7V0xcBpZk+435dyOf1Kg6mSlcpVBsfmBqzr/wbJVJCgxeJNlqFolaxYJLEe6WkmbnGADW4lcp+TXVq2k9Z+e0F+1cnZaXRn4Q+erzTVz33uPgUEaYBhm0IidiaRh5r3urx9Nv+5+3Q+q1SoFV4BAgECAwJ8dgQd/dgAC/gMEAgQCBDgCgTIM1sHECFQqWX0nHqHLsk6h8xqbeIDgBV8iALlqO8tRdvnqmhpJplRrNd2XhHpEVKAMPQI2GDZAIEDgfiEQKEOP5VVZ+qyzVEPMkj/WabVVoJzaoDP8H8sfUyJ0zrIPP+s379kla+nzmt4dHgNuU7tZJNqJU0TlM8g5/Wa9zQsmXvFhWN5dEQq5tiDXSGeH4lGVzoS9FqPtVpPUCPnKggMmmpJuMB005o80Wm1/RStqnZpivR/RWSOltHcK1yvFBjPfq1bHW6GG5Vpq6iQh2KLWqUqRf+3QcrRETT4pcNlqnQIXptQmtGwDZWhX6zh8rnYeYnp7W49HVLrYKNDRXp0SVyG29/CDHlFTfIXoD8urlKga9zYo027qV/v2tp/noSo7znOFiC/HXpH2azVWqezp2wf+3cbOCyZe8VGr7bNKs61D85FK+MJzRUik1Pav9OZxXlOSF2zLh4qQf0WAiaK1drTlaJFdvHlJR+92qVncVdo/xK+jxTSLxfLaUWQViqvevfeGbbeSmhqpjFXqwEWpnLY0aD5W0r+nT1wRMonL6dELKOEL9v0nZ4qQ0x4oQ4dKzslri+U6GUounM5QjP/0Z1bp6nxf+N3kPZUu20ShCSZI1tu0fREhNbcDy7Cid2AZHmTalLgH/rx5wcRtPrhCzH75VCsVL1kHBk8UK4TnfXRaFzC5yqRG4dOrVn3t01t8tSssNO57DGe/FOtdz3xDaioM2o17RbHeuba3c3GFmP0CuJT+j7VhH0ZIuqwFLi/KVAIuf9iwMq3mCpShHQl4+MxiNEx0Pt0EwpLY29YPYH3mCgcYrIztt1SwblwDW3EMuLa2JodNiSlMX0hYp+1mT+E7nfs+YGKHt2n5CKe+pKdqkQ5/2RVYV3QEOOIf2NZektQ6YK/V7JAx9Jknn9e0ZKOrTQbkqvB3tK6U8SffkkuLa9qgymIkLLf5U5AujIZSiX462aU0Nle6CPz8g229/SsV685hCZThVMvJPy9jq8D2tmPYehMUUhIKaUoNa2KNb8XN6aijosmwfH0DipeYzITJcIoyT1VSD3/hvzxEv+SpRBn6hN9PeIan0SeC/F9DVVhofU5GRZOv3r8WlqkvrnCavoiVqPTTCQlteLxJJf0L4DLd73+gDH0h3dFEcOVzUsjh61CmKgIuVk9XKkt6If6Z8vkGfsELdKzX9XP4D/mz2eySvplLUUPGVHqBm3vAuiWJdvkZhYkxsB1svcRp1PxiSyi2yofsSNO1k5cKdoLXfMsstplStk+0zVySmWXLgxR+30IPwxSy1TZX0qyBIIlcqzLoYg6w9LfKPwGXpHby1Y99XLpBE67YT16usLT+Lek33h82d6AMvVzpLozNI83xwiYtXkCTLVoPKC21HC3sNakYfk7USFGq8ByKk0goBLZBC8dtqsI3mUV0O5KaLEjjAhuuDWGXn1GYGMTYwdY1wi0GsjN/+Ovv6IWapI0fFrAGXtDzOqNGd5tZqTzRCsprtnAEpxv8cO2TwnU0uYGAhI6AhL+izHZwhGy1l8oGW/j5E+mpiNLh/KTfIFgkAyzm6HC4WKZ8KU1vdv6NFv8XuPwXEXbIwloGrtpyYZM9vmiSPuQ7Y0VPoAztSGnaZ9qXIpXGSi4Xrc6tYIn53j4izwkotexCTG9c3iZEWhYRGTBBBJovhvpxHj+GKfqwjYgk/ImhaoIHacTL4cgCPEBwNt/15RCTWu18LD/jMElcSX/qOGxtQeSQD7vz12q/Kn97QVpDVRkcd9QwWYX8s9C6lC3f7obDj+kp84NsfxPr/bEFgBftDhFDtMS05zbu1arnyl84Px/fU+0jfsizcq1abYWwDpT/eKFrjVKJIZcGuPT9mZCr8kx+Z7QfL4nZjTIFytDWinf+UCX7EGk10hXdgBMceX96PYJ8MTj3xK4VP+GLQ+6Nyw8czEfLiZScYviECkzOd4ax4UDUjS8/v9c5QoBle2/qIIdzRPgidw+Tm/w4wcQpL27yMYqGv/4tTwypquWvI5Qa4SzsHP830dYeIs39bbRT3py+V8k+QlrNmsgzbKQVnmuofZd9iGyYItJp+HqPynvR2/fWUoPpNUK2W+9E4ObKImcw+TxP9CPRq2KYe1Sn9qEGytCp1G2+x534CfxsJ4znz2vIxSLkFY6/N24KHkXGQATDT1w8eMEtwxDG7v3wXkmLkF98i5w7nD7SbMwLZT2ORMvP3cLEip9JMXHEQPclt/iwRUP+OaWU4ek02Seftdzfy+ysEXHsL+S+OHq2jiR9BEscxt9q+78rz9ar9Mxg6uNreg0rz869Kp4zrVVt5bDMmpyfqxEJ2S+eU1rgMj5pexzOjpWh2IrsbNLGwQKVkRRqOOvHTej08yySlHOXGSqvYi6bCclO55rmvVnjYpdWgZ9QhNYBGLvj+OW5eePHjKvh7yThA+7gQFEOBl99aDpN9tGHriK8v4ETM/+QbVcRJgeUnIx2rzB6+z9UjPyL8Ddtvd2dOJ1GjH+ZYd9+U6QUfKuGL/KBdEgj0jh0led5ZHJA2RlbkYPMMeSVFKcevP6S7F8lWHOV9HguTovlpj5uC+k1PVbje4WL9IHxrW+LspWKPine/NhY3KQI+f8FuJv9iKEdubnJz7TY2qF31DPD5z+jg02kjmADqC4eIynZ2iqswCKMC4tQKkL+f0GvM8TQXLGWpuVv0vf5cb5lYRFKRcj/f0m7rI7CERWCvxHOpYP/5Lj8O5Ue/0w6kqyvLKxCGU1eh15qUUtLaRHWD8BAlyinq6Qtr8TZT9+eao2K3J73LMPYNhzwXccyZ8A4d5k/HqYI5fP7fM83o4tvS5p7Gfjg4rQwwZG1WZDXV4Tu4sItINb1AcLhQpGGiqOqg37A0V82/mO3hiUkzkMLXzJXq1yu9/GSP97u8DMtttPiN2z+SndgKDgICufN60kKI8kaFszAlDKanGRnujBlNJ4ML2WLJG3LsMO0FHv7vowmr7Nmj5/uWj3i/PSvfzbSYHKLPu2mKGKRZM0tP0WRfktCZma0UcIx5pZ21lV6/C50iXL6LgP/5jLb/nSqFfFZVxnmqQwnpOECMhYcPyC+mkTUzazvTjZJPYO12Ow/7y1Eg6PLRFrSI92jZ5NaSZ7R6hEu3CKuGk5Bg3iTH3AcPzL6avIhGi849PeNm8/rz93kZ1psp+V12PxC5/V8wVd852U5lYwmW8kWPj/fZEjbR4lHiP+yvn47uRt+R+5PBArCp7kuHJJ/0PvX1rhwy28dUemB64/3lLjxOFeI77ZIi678wFKnRe2BXFwhvg3uvdvZ2YAd0T/4b3xgWD/46bnlI3RaPcWqQgevvBLmFTqMiCunxXTMS57hPaCjDg+t3f01Cpe7py6gIEAgQGAYAvJo3wEdd76+XahBpgtgQwWFd6tySueIDvhHZZiL54PbY6fVU/oVOlBogGQJKsPaQ4UOlL+6uH3eFcdxMjGVDo46/SjtXcp7BC53SVYwd4BAgMAYBLpH+w6OO7eV4ckmz3/DNhh+ivOb/kCRYBqjDNLXrixchU6rp4gKHZmYrqqXxAtYGJdRoeOmUubPLy2SfoZyFzwh2e51s+DA8PcmLDgwBhe79AXPBQgECMwWAZ5OtPRY1/552WYDqTUiaAIPbGx71VGqzDTVU4zyVYcniHICD7n1/ID84BFFBy4QXa3bj67eLDgwCna3Cg7AqW03AX62qyCYbSgCiMrayo4IZHsvF5F1HiZ0SU8Z9vxeCJrsIZhiVXxEWGo4VDaq6pTjSiHdra96eCLO1BIPSKBCRxsVOvppw/4EfxQudr9Y/uQsoGoUAoFs52t99JRhZyeHKDF3FfZ9djdZDUf56doLwnHaoZedSiFWL/e3yoe0hIorJwUcXUPDITejxV5tk+3gMl/LJuAmQGD+EBDKsJdKg6CJORFX3j+k5zeSrofBYKdSyCgIRSUKlMLf2OEVOvKo0HErTjP4+mJ0ImV5F9vk+VsyAUcBAnOIAHSJUIYnBX4CBUEDJBWai4LKFJtFem7wLiqeNCzL0tupFNJLo0FGvVVdPp7mg7PXOip08AIDFBpyskUqae7bHBLJmbWsRuAya1KC+dxFYNyadXe2YLRZIyATvRl7+n2EHshUGk7CGa8Owf/oOfxl7RNT4ambfr0u5XYrhRiZ9aMYFpUoeIUOUxL4rec7LWzWEdVOh6G8Zw2fxXxDcPEBZQEJAQIBAqMQELrkqdAlD25V3rB40UjIFtHicl5XU9KvZxRnsF8pZEm/HJKnODAtKnSMKvzAS/ucxTK055PgyjBcglU4Dwi0ydaanQdW/4Q8CF3yNENv0TJg8qo1yVXajkXg10N7ywnBOylsoF8Btr+mrm1WFTq2UaFjWA8Pw5Ldbg8P9ExIljuPT4GLOwTMZhRjF3CJ4NZ9LfQwCVJWa3aS9+/Ts7IqTJRdvrqmBgojTNv8ye+8Q5fgbDKxrU9fi5ajEytD84kRVK3R94r2q9achxIs1K24PAjUYIWO6pASXUIR5g5QDHX6DmxuC2oaXNymJRjPPQSGr1n35ghGmj0CQhGuHLDHP8uuf7x47MTKkJNtfPGjqGeYi7dQz7DS2zI7ZctcocOqEg6v8BHfRD1D1Hjzaz1DL3DheBoVhPjfqJRNq60C5VRRhabX3In307h5z6ksvH5v3viZBq9xWPDSXO2d/HWu2GCGvP3c8ImX3FLSDVExBhWtabX9Fa2odWqKtSqbO7V3Ctcr4Md8z43irHblwKvaLG+inuHbpqhniECtiJM4UoaGQuStzhOJq4EiD3YJMp4b9DcOr9DBK3wkQpjLR60orXgV/LiAi3ns2nmI6e1tBLpUutgo0BHcCAn0RtnDD0QEqUhYZfrDMtwWVeOevxs+zRs/k655u7KNQraxWF47iqzih68OJRK/jhb93fAJslW01g62n0V28eYlHb3bpWZxV2n/wGlPM4Ofpg5+xL03aGAlGz7NalvOq9o8gy75+L5GpuLazpXhNAsgeNc5Aotl7k+VxXTlEUbYC5lV3hTIdE+1TH9yPqt3b84bP9MgdROLpyUu229IRec7bjkZTeUvOzBk0C/UP42MrblefLXbazwfzn4p1qpu5kfcK4q1SiKj5W4vx5bh3ZIdzG5GYHHU+cgpobp5aocXEBUXmlvhMp27nrC4xQi6vORnSjhm/jrHotvu2vW5n3xe05KNfhXYvmwVPpfWlTT+hGxb0rc2rfW2GAE/3VanrjM05YCBMpwSwHl//eapnVHRZLeKW8w7pn7h79dQFRZnn5pR0eSr9yiw6hfCPaIjUIYeAeu3YeUJoRw6apQtT//4jd5R9GSzS/pmDqemuiZTDMdI56XRlRM5iH4fhRw6GZV5P1rH3fGczO32O5CttrmSZg3RV7QfdJlFgCVQhm5L04fj8UhzvLCJ897QHlad7H1I8zCS5FHMDVpAvmoVflLeLjSS8nfAyEt4s4/QEKqwyeZEtjgat8EWfv5EeiqidE4K19H0G7bVDbAYXey8wjNQhl4h6/a4ooCstS67QBmhmzVuzff2EXnmRXCzCzG9cek2YQ7Hc8iPbFOR4AEjMXFYnAvnpeXu8TUGi5vRBS5b497+7yFFyPZxTPvxN2K+KJ7Z/k2s1ccWIrlog3aGaIlpz23cq1V5DxTI9uN7qiHMW8lK2doqLumC+ANl6AKIXg8hT91Id3YDgQvkGur1iKlHjBpBIrr1PT+eEnGTH36cChWAb7eo8FooLo0/Hoso5K1plchDikeLMvigyntrKaSjuNA83SVWxDCV7COk1cjOdI20wnMNte+yDwmpNiR2vpx2fi96+57gp5vzx8cSst1610uKdpNOq7ECZeg1wi6Mf+v8ODrb8Y4MCXi/e0cih9xzYfqBIYy8UChZx0O7xQ/fIudEP2iZVnQfL3tYvJbyRie8vrzd74DHS+Dz7nOhc4ztsANwbf935RnoFA3s+IXOdq9h5dm5xzvgGRdk220kH1GqVzIp2usrUIZeIxyM7wkC/ESSVITn91YRegLMHAzKT4ismBrJz4qlQBnOCuk7nkdGk/lWG31jKvb7xtwx2ZbT8yNscZMi5P8XCL1zTAVA/Ei3VzTJaPI6/IUtaum6Bo+c4nWwwTNeYBEumxQhP973knZZfQaFIwJl6JVUfTQut6IY7/QlLpUiDRWFcdt64ur+bS+NquxnKHoJJ73YPnHO8scoi/4nvLKPPmgKg4+uK9uokG1LO1vznz9xnHhkodV11tRR0JQnfUOwQrZHu+NedeXz/wfAX/lhdIhUZwAAAABJRU5ErkJggg==)
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)
![](data:image/png;base64,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)
Question 8.Find the coordinates of the points which divides the line segment joining A(-2, 2) and B(2, 8) into four equal parts.
Answer:![](data:image/png;base64,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)
⇒ Let x,y and z divide the line into 4 equal parts such that
AX = XY = YZ = ZB
⇒ X divides AB in ration 1:3
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZEAAAAqCAYAAAByW2ZVAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAABmQSURBVHhe7V1NbBtHln7V8nEB52ztLWwatnVawAFMKbdZc0QGGB8iDUY5UAEiyqewtWvNwdbQkizvIfJYki8j0gNEOkSGmQTrACIV73EtMsDKBwPrSBDJOfoeGfBpwe79qppNkVT/scU/y92AkMDsqnr11et6Ve/33MLCAvmPj4CPgI+Aj4CPgBcEznlp5LfxEfAR8BHwEfAR4Aj4QuQD4oNkckLbWVumpcxlmssnaG9xkbmZ/sT551psf5zmZtFmy10bN/2ehXe8Yupl7hMfPVdjv44zvg6RAEkLi4ual376pQ2wU8GPTPDjboJGGUmLLuYEflQn98fZHeAwChzctOmXOXeajmTyi8rOo2XpfuYS3X7xNb1jbOBgcVF1GveL888rsf0x6fatBL17hTYHzm2MPn0h4oRuB36fuHpeW17K0OXNPB11aVPmm93asEyZ8Rxt5kdpqypA+L+Xd7K0vKRQulCdbChOq5upGm1bR2GWnyVtODZMQ3N5bXCvPwSJTvsyxZbSVLCgvQPLV+vSClMvY9qtg1IVGFu/haX8LFOxDiw+l1fv3k1KCwunFyQTn3ykLt97yjg/GmN5mUMrbbgAWRsJsszYNm3kIyTTsTCYuPpGnVxKs7yxphSi+MoGpRVZCE7wo7Q7S+rI5DB7dmdXTSeBgwvh0wp9Xt7lcyrvPGCT99OUz1fle2iKVjZSpMis48KOj/9oRGaZz7fp2xcResVICBAuWMo729KD+zOUBl2Csipdg1WB8d1ReGD3z6wyEvtUunL7ReV3l5KuBYkvRLxwi8c2yYmr2nQMH8xd3kGccgGiPY99tdLseLMrUfhoi20tHo+6My1TJA1qciVa2NtigkY5AqYnymkpzbitLG4dsfzmuDYsD9PlUl47jfAz6Nmf0+g0AkmnPUSroD1cpX0N+Crya1o9JY1O+Nph6tTW7HfTdQhW10FNqZHqRrm49ZuU3/yjOhwcZqvFvKrI3jfQ5MQn6nRslNX48WMSG8yilwm00OZYgBxSAYLhydGxIOS3jGCU2NR2kfIRXWhwoRKMBlmIiurdGg5H0u7GuDoSHGGrh7tqAv/u9UZi0LN/u0LpCPMskPgaRh+H6OH2Ie2CdirvVB5NRpkS/JWouIvN3DuNTvDqAgRC+fNDyg++Gnhy7/gmsTMdAF1EXwHTp+9eDYz9yz/93005Kv1bkGi7kqpckiAwIGwWvzsa2N0cq4zIn0qXDl9ULpE7QeILEafVadPvyYnz2vBykeY2NZrNDpOsuOs4mcSmPvyMbuRTpuonXTBZ/y5GwWldKUBo5QPow2TceA6b+ZZQbS1u7bHZ1ZCWVtL0bCdFg3Wvc0GyuUqaHFujUj6pGbcZdzPp0FvxOTqqo31iPKQpuJbsl6iB9vrRu4Kpl+meXAf1cSLNnv28ThTB8lR9YLggwTqowck1VswnVNnD5pSc+EgdXj5kBj8GXfAjcFOnR56xGy9Spqon8KJ6c/IZ+8OLdfxuc/IGP84Upmj7RYAiCfBclSf1zXye0dQ2paMQINVb1tbeoJSdIjX6fZYVE0ptvuBHaWOF4/CIRXYTHd2kXS/n1B2agQB5q9+MpImxayr4kXF+5Ncts4fjehO4WuHmCtedb/CNA9P/DtA7SSYIhcahprL0GALknw8O1MUDGphduVZJzzyWOG/967tjrTYXJJsrWkX+ck06fJGoENMFjN38fSHimjtO9yLfgMPYkWFTIPm8fqN098h0mdIUGcbNIH98M+BtxWbIIvSabz4W9g3jxIyrhqkQ2htcYAtN96FAcAi913QJDWQGouMUUjKULePr7/FjRntpn9MdpxujwNrymtdZTL3A0vI6RP5I15SnlCslxK2xVR9LLohq/PgR8U3ChX2M4/aYIiNE2d1Uw6YtBIwUZa8hAFISTvMWajbj1K/hvajNe6YYDgUpKMEWVNe34MeZDOXKX1NCdjEFL4vjsg3WUJqnl5CK+Ks+pV85P04JfrR+dFyjIxptm+B6E7j+71fAFYLZTG1n3EK48I3++MPAAgRF/Viga0DQdXD8rx/jG2f0iylJH3/GMf1efOODr5wn7wsRZ4x6+sbiIlRM+ZJGsGdEhi/XbgCGAElDOCwM7ll/PeUsZcDH8TnbXbVhjjvPoN+y2ogDURoPKZTJlincU2QaB+c3srXlJVqiVbGx2jkN9AJTL1D9/J9pnDYgEH/PKN2sZwpEaPwa1gGqPE9SxANBwE1K7hZVgtokOnIZGhr99I+rboULkDQ2MeiD7O005Rx9X8Csbo9SOgUi6g7Mov87U+pMNMriWaiuIrqqTqiz5kPs4eEoKWjTcMgGP46FZoBDmZSE3LIw9QCDqyb89vDowX22xFZp+/BrXCStb2b1uH4GXA/rcOUCJA0BonFcrew+1W98Cpj+DreKAxcKSf6Na1y4gbfeYQUbmnz8Gb5xYIpvHKoxR0x9IeKKJXr7Uv2mB5MElTa5iitCXICUUtxIbmNZKe3jThGicZxWj1wYYITaDe/Gc+bqM07L1SHSCrif85Nsrx9DmDJhZ4K9MD5OsgtbUzcx9YKRWAforOO5dYo0nb55f3zj+WRIUwv7ZRwg8KLjp+6FipNt6je8IG4kxc2g+iAWJS5AiinY+5o3+eYuSr8KfhyzUO0sQnVVzK6qk9GLjDRN5ct6F++vFHdNjdOcnqtXNPWX/RIj5uFK1h5Yar0I1RQ2fumubsAOTX0u+NHpqcf1InA93Lio/vVLHdfDdeF4YC0aBKbX6HP+0iunkaDB+OI87B5Mmtpep3c/nvTEWlz8bgCYVgoHJclSJ1w3jC9EnDHvizcaNj3OLKHVqgBpn6dUTfW1WnI2eL8u0kTKnV3k6pu7GjfeG8/du9Udn+v5dVtu9YGRvNSax9ri4h4bRMAsV+dwr7dYRCE5vd/gFGC1gJ3CtHm+1gxkPt/aOqwUdUOvnQcW1qGIzbbeu6nTDNsgSGQsH3ixqG90no3bBs0QnjCWzzDt4SG/Yek3EW5svyixg23V2hOL46BGVJk5G6+xPmo0TcxgvBo/RvmRnITg0h9r4WXNU3vShfl5mtf5EcJwhgUf71MWzhFOhvUGQRKEEAqtANdRgpbu1LjW8IWnFjy4JAK+6Xc/Dgw2qb4a5sUxXU9UXjm4CftCpNNfXI/7Lxdfg4IhCjqczo2NSxmCegweXO0kW+j765T2dt5Z8PryPPTWHjzIcnGNQWItrc12TN3mhGnzfO0m1Dzf+nUgJQgBstCC/cwzdF1rWC6BH7UhcTpv1tAZ9pLCtYd0CNWUcfoOJDZp5fsgzdxfo+LosWHdK9HCdtHIj8Ld2Mw76+2Tey6UQ+aUgB+l3exXqhT9O7sPfozCeNWq7crNHMtFeH9Vv/F3NlcW7urLBYhyBeoxeHA1207cjGX2ji9EvCLX5Xa1zQU6/1IpSMvcVZirthy8pHQj+Wsqlu0J5u6JXIA4qse6PO+Wh5Mv4/zo7uk0pu6oaHyrfh0CKQ1qK+9C1cv4btoYm72i4aQMXuTqLKHacuEhFZDBj+w1lcCPJ7VPJTqA/U6bajSgGyorSh+wEkSP7MYHwM1EuvGOfEXwo5uTgGEgVzQI0eJF4uosodpywDUQvFL7xu0M4dzVV7mSFeoxxJCc9ODyiIcvRDwC181mDZsdIs25a20qn9MInlnydBAbvzu1khXNPCJdfg7hVB+EePWNNlzEad7qVgJPmV66+DbHadTmJmxAsCU4XL06jakX/jBdh0/eqMOHs6ygBMzVWtxjiXvtdOnG0iBAEGXOVS2pfLZCsAMEb8pcreWotrHGRqZL2HEZ1CiHZqqp0CVrAWLiueVlDby2MQTA0zHEviR0NZzoS9grEKMBfszjv1ZHggYBInBl0vqujutFfOOHqdPgSsQj0uX/WoHb7uhxEOLVN5WR4i0pf8HiVsIx/eGkt1czRr4Q8co1p27nfDvgQ5htdvzfuS0gpVUFCXEPLQuCxMk8bRk3YRjSV+HRVB/Fzk/EdHn2RKe6IZurwV1a6k+Nk30HBSVG49XAQuGhFYNGGzr6WTijbVk4EnQaUy9TtlgHdWc6yOjyLZN1QKCgRCy0EsAm1Y4QQZ0fIza2aTMBUg3wk1JqVhWChISHFlnmdRUnc50fm+Mm+I2Dx1XMzMywybUgbSj6xlnema4E54lde4gbD4RWvZeSbshm+E0mOH11PlLSYXF/USZpJbKrKtxrTQQbIu4F6jnOj1aPmQAxcF2v4noRuMJDy1wdJjD9Ox1YxEYZhvSHhwl69YNuSBfpUW7CNnLJjLeuVm4OMOnaX4GpC0u9L0S8fPEe2oiNazpGGeQWMQx3SIWADS+kxcc3adDqxF8u0f4QN6Ifb/LG8EKQlFY1QhDjRNLiNlJ1yVWe7ZgKmp1lRZyUCrqPvTg9GYZG7MUnn3IRyjF4e0UDSIviAYg2NRFG8U0IUbj1ZkA714Jwe32o5rFm43DQYUy9TNHzOmDXL/CQnRa1XkIgTMdYAz9ihwY/qm/Aj2mzmw/H7cqK4EWYNBqMveBFKVVcVdlyid1SSQ1YGbjhmjwGF3Hlpx2iaOSEUxlPaVLMDiHtCQTSjEBSxaLSSrZEymjgpIFZ8OM1wY92J30va9JKG2EU34AghVvv04sSzWgi9gbeWVAfca81O+O44McVOvzb1+IGUh95z3FdL66g3xL7d+5AYRZYKr7xGYFp+nfvTgianW/0bzyPIBs8lYZvfMVklv8Apho86ICp8gqBiw7M5VmI8E3RSzK/Vham/t33PQkg3/RoMEzhBfw1g2CzG/MI8kHcMnBLMIWOBzHa/s4327m4pkSe0dW6NCZGZ7ZGYBO6ytkMFULjtIldxKsMEViEF7gHmFd2EO04Nicx3bN3ea626ySmXiZlvw5POFwNTzn3lH65Nk4buDl4kCHCRdiOH81uEsBbssftN+kC59V71ut6HAvyE9tWR9WIibDhEerXMeHrdR/K270tMvNkF/wIHL4NePcFEVhcn6fBl/do4ThOsOVl5PjQhesUnsdfrfVLenLPvlPe7sIFwnv3rL5x+99FfM1XqhL9iWX/tl55JzUmXRTBhvMW03kL3nrb+Ns/tvk3PgZM4TFs61ust/MkRI710Y3J/FpGvYUG/ZoE0GwK3RawjjCOztJqSD61x5KZysVx7LP6Qpsw9QKPSFkSJLYC9QQiRDznevIydlvaALuVUJDuP7qleyx5dFnS3YE5DvwE3z432LbMsdudjP4Z33iQ/gOYugkQtCLPTPXF37XL8ntOGPOU4xQXcWgIeFK8JAyr3FVSPDwmoWrQbTZo2ga6tRnIdiYBbDNpte56IWCd5lIfD4Esvtpm4jiLr1Nb43chQGIZGsq1Fsfhtv/37b12YOplzkKAxJ6yoSwy7gYbU4B46a8XberjIWh1W/1TItlyjIkQIJMZdiWrByEe9UEW315gaYzZgOnn25U//SVZM6C7pUsIkNj30pXtF0h30hiEaJfl9xw/4ZdyQ5oMgRGqCzJD5CjLxUmLwGiru31WdcxOyfzcUuzxvb5MAlidSy8FrBOcxqYXRD2R2DASQcI1uJV6IsPLqCeCVOF+PZFjpE+DqdN6mf3O64lgHZA0Ma/XE2lDGngvdLSjjbHpgR/Z5HCJ1xNx7dXFgw9HgMOdjbyoJ4K8cW48aNtBdl/3oWNaqsioJ/LlpyVeT6RyKemcQNG4aYx8g3oi376wrCdileVXqLMC4mqeJkVZprmq3lxXXSDzq9ZYe4LXpLBK5tcthPspCWDDnHssYJ3wF7YI5DEIh494bimn12u/84NGeBBtThEI6Hqw9+xFr5h6mSavJ2Ksg0cNkJdhO9ZG2CIMfoQdxUVWHkELN75fr/Kj2zYdm0SfdcxTlhBdoOvXj+ilhY3FjGR+07g++JZeIrjS7jHL8iuEiO7psqplkJ88Mn2DtJRewGgIqq2G06pNMr+GVA9V9Ret8ZTnuqrMUJM1E1hzt6wVFdJVZ4HyGnIO6l4FPP1AQzqMPkwC6JQtt894zSfHR8BHwEfAEwLNWX5rhnVdTRSCfWSJptH1a0Qvh5sr2Nkk8+PeJbk4z5GEDX9Td0dNJje11YxMdsWH6nXLCo/Grtpe+Oz0FBaiwFBDBUDepp+SAIqV8JAt19MK+o18BHwEfAR6iUBTlt8G76xAYo7iCrLDpnU11p5ddliTSYymSrT6GukzqkWLyriJZMZ51Tn7JIFcKIhiQso+8Rgk4xE5injRIasSsi0kATT6PG1yPMu1azFbbi95wB/bR8BHwEfAKwLNWX6bXHxRHIUneimYJ7BzSjxXrxaLTWfQ0RzShbtL5qfbOZRaNT1dPfQct5pRCJH2aT5PkxzPK+gI3vMNf17B89u1goCr9CfgR5dFqFoZ2n/3jCMwgNQ6jRUOq1l+G4RIeQ0R1eM5yg1FKFJnZDfAcZPM71gtRlBDtSAAmiOruZGaxql0iqC2bi6qnYAF+N4jobo5CX+sDwIB8KMIXfYfH4F2IFATInocwBBcP0dptLxKobRuZLfMyWQxul6/+g3F4/D2kqdd1XXgXR2rtPTI6h0kaIrPafZJ/jwkAeyUOsuNgG3Hgvl9+Aj4CPgI9BMCQogYnkVD2LS5NxZXHulG9gi9yWkaDz4URDsl8xMqqBhdhh97InBDJGJrRRAZNpmltcs09BplQVElzaxO9mmSAPZCndVPC+7T4iPgI+Aj0BYEqll+hRDhaizhGVWX+bRmZI/gNlFKaSLIzCaZn0j1gcyvwpCOd3kUQgreVelIhJ6vljSeUryh8JFJXXCeUPAGAhzTsI1AF0YIIjJXA/VJEsCGhXAQsG1ZNL8THwGXCIgEi8NBpgxlq3XPz1ZxK5cw+K91AAEc4huy/J47//yuJotgjALF1qK1xGE70/DSEgSkkR5auNlqyC5pmsyvMdZDT82dCOzQdLXwdQH5cdCBlnQxoVFIET7wXCKAW5F5g3YkAXRBSmuvOGTLba0z/20fAR8BH4E+RaApy++5ozBKlxopJ+uytjarfWplPE0SzxlZWY1++Lt8/zdqXwsoRN9XtX0IrPgcrjxmeioDs/iNxiDHOiz7NQmg8EyzyZbbp+zgmSx+cCjD+SG2lKZCLVA0Dm+6lLVLtufRvDfkddeXlzJCxWrpKu69+z5uWab9XzR8a7+Hy34fFNpoE1L8hgW+Y5Pgu3wd361srIscWvVp1Ns0pKdueH31B/cz7NK3u5ToI7o8TaapUXOW35az+J4m8dzO9BJBNyYSPBp06beYGIww3I5SRpB7rLoRnXTr7fskgD3M7NoO5milD666FIGlWM/wHgSoKAgVwYes31q9btjGrdYuQNUNnZyeaV5CWBRvQdyTQ415N32+T+/8PI30FajBkY7wqodnJ7cU57so+O5htki7ERRVQuGntckomwkipqy46zr/Vv1aGsW2zGqst7rm4Dv1JugJwqtfoynKgu/O0mOW5bdlIcIB8Zp4bm8wzAZRF+DkU6DMMorUEDYhRMovmAQX8mzD/Z4E8DQC9r1kNB4ICgEieAK1PUTAKK4lvGqdVaHFbsxTHDZQqGtuU6PZLE+9041R+2uM/xkMS/xb85pmvb9m00RN/A7NRGXprS4c9WqIhQLjlf1O1m3v3kxEZuEHRXb72wrdyn1KwZmz5dlvleXXkxAxBImXZH5WS1qAJxfFeQU/nvDx5C3kfUkC6FXAdo/V2zOSUHc2pcwrcV0lTv03HLSV7aHAuhceqxSGFOMJI+XzerVG/zkbCIDvpHlCkae66lGC77Q4/QF8B4fOVos8tg0Y8J10HcWleBLD4HntTAV08noiVll+PQuRdiHfaE85sqzg167xutFPNzO7dmM+TmMIVRbK1C7Bwy+HWu1uU8w79ev/7iNghwBXHYHvGOe7LPhu9EMvTNVBdrHL8ttzIdLBeftddxgBPV4nQlUnPJTCHif5A7M9dBhiv3sTBMB36k0pylg1m1AoPkaBj32oeoWAL0R6hfwZGJfH9RgeeNwLKhZRSE7vu85SwCFoziCAvE46MhGhT65TRTWVAzgD+PlT8IYA+E66gKLhvKYK94KajM6wYPqAsuq6K8M6eE6NpokZzFXjuajIBqNWORD/G6KVol45sV+8vrwh1tlWvhDpLL4fTO9be0dMT91vnrzTCohmV3I776yam/kHg6o/UScEwHfSbnZKlaJpdn+tWrPdoZGwq9RV9bLzznoL+4b78m1O1J7N330hcjbXtTezElH7/uMj0GUEBN8x34Oiy7Abw/lCpEfAv8/DNteSr81F1FSBf1bQN4y8z+vbr7QbN4bM2CEVErK0YNRWF3yHqAzwnRF/2K9zOIt0+ULkLK5ql+ZUUPQUNzywUA82hDYZpZFn63KwdYkUh2FeU7HcH5T4VJwegV+USVqJ7KpKMlkNNpxndG2FbsE9q5cuvidnpvNdBFmfzvLjC5GzvLodmptefCynEdx6MzLjpz+N28ND8Vw1zse+kmWHyKp1K25K06iNky6QYSSFcRQEhrT4+CYNIhlop2nw+28/AuA7KbmRVcF3LBOUaAZGcD5KKJ6lw3VkJ+ixiy+/KT26OcmepvNklKGb4XSGQurU+AalcXs6iwZ6X4i0n9c/iB55hDoNhimMhGlG6jWE95kGirYCiBE3hNQ4rTRreFf0cYK26it1+eE8D+A37BkC4Dvp5Nq+pCf3EIDo8eHCia7P0+DLe/UxjC33Jvq5cJ3C8/hrbn30BJk+Wu7yvWjw//Mc7uOMpyZ0AAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
⇒ Y divides AB in ratio 1:1
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Y(0,5)
⇒ Z divides AB in ratio 3:1
![](data:image/png;base64,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)
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)
![](data:image/png;base64,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)
Question 9.Find the coordinates of the point which divides the line segment joining the points (a+b, a-b) and (a-b, a+b) in the ratio 3 : 2 internally.
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
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)
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)
![](data:image/png;base64,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)
Question 10.Find the coordinates of centroid of the triangle with vertices following:
(-1, 3), (6, -3) and (-3, 6)
Answer:The coordinates of centroid are
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 11.Find the coordinates of centroid of the triangle with vertices following:
(6, 2), (0, 0) and (4, -7)
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMIAAAApCAMAAABQvAZCAAAAAXNSR0IArs4c6QAAAH5QTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OjoAOjo6OjqQOmaQOma2OpC2OpDbZgAAZgA6ZjoAZmZmZrbbZrb/kDoAkGY6kLaQkLbbkNv/tmYAtmY6tpBmttv/tv//25A627Zm27aQ29v/2////7Zm/9uQ/9u2//+2///b9V3zhAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAC4ElEQVRoQ+1ZbXPbIAw27Vq2pV29rXPW0m1uFr/w///gEGAHJLmE1dzVd+VTDotHetAbkKp6H+87sPYO6Cd5dUyB6r0Qu98pKfjeXjxGYvrwTYgP8RyHk9DQCjtYSzt5+xdB6uYHmbk6Ds3ln3iaylVVLxEFJe6roU4u1Q2n4aRPgUm9xIaBQCfvyZ5Q0zqwqxMIgKEw1t8xhWtwTXIprwGZ1uKdgO9jDRqSXlCwlsgyFNSdtQWPNHteQ4wz1ndMCBJskCGmgZeBAopExlu7I0vBGhgOvHRBQ7wIp5n7qi5/mmy7jdN5gYJTEwwiN359rDgKNIZ5CkQDUsdEjNlv8eVYHeTJQcplvhlBQDjoSAEnpxuDYyi0JGeiAOCXRhpYK9iImaxS8fYuBhLaBSzXTexjCrqhu7cUSNw+T65AVvppv7Eo02mM+2RD2cQVVSaQ1DVtO2QpryEMpD6IlXDe5VnKC64opssKIJNcaMHFXYo9r4GaSktSL80WPaOqTXcXihHNNdYLuGz0H02R1SpFgdcQGMxXVBDoof0/vFzxzNfBiN3geOAomHyIG4PPzBQFXkNgF1usmTaxsSn9a4f6zSYItDfzaVM3piNscfSffc22bWibwxYIqH3coW8jlGyZNm35pT74xqk4N/CXhzdu+mSeS4JtV1kFIeQpzMfStX/M/lwbWACyPRCxV7iNxJGnsPFAsidH7oa7HS9ALpSvSAXLtju0FlTgfVlQg2/Ped1ZP38660kuCMWx5p6t2FjNRXfd2bgh54ykLh6qocnKnyf6xLaUa5no0xnJcMg4qdpeQp7k1kr/PPT5pGr8kHtfIO9Za1GwOOeiB/eFXP3D/nTXyF2bli+LbvWPNXN3Tlt2pkRZ9JMRB1nyilEWfWLRiZwidqYDZrGy6F7N0nNarrG8fFl030T4Z9nXE/A3GPwvyuuBQwQNXW3Ab/Nr6SiLPlk57CX5F2ItBuap8D/Q/wGw8UA/bJ7GqAAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
Question 12.Find the coordinates of centroid of the triangle with vertices following:
(1, -1), (0, 6) and (-3, 0)
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEoAAAApCAMAAAClbk+3AAAAAXNSR0IArs4c6QAAAH5QTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OjoAOjo6OjpmOjqQOmaQOma2OpC2OpDbZgAAZjoAZjo6ZrbbZrb/kDoAkDo6kGY6kLbbkNv/tmYAtmY6tpBmttv/tv//25A625Bm27Zm27aQ2////7Zm/9uQ/9u2//+2///bPsS8UwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABhklEQVRIS91W2VLDMAxMCtTcECihYKCBEjv+/x9EskOuSbQaJk/oqTPdWUtaaZUs+5fx+QrKCseHPD+VUc7kFBtEZfNd5ouTg/SiM0+aPtstoapcxCqp4nP1elR2lQI5KVSAM1dmXhrLesRIooTyXu5qeCZpSqggM3HnYTgDHiQGu/2GPARoCvhidUZMtfii5X9xVu6c+hUieDEstcmXsspcXhJApPKPhLj50LThT5jwfi1uGyCt+tRCeadSa5HRXbbLCmcRVxpV4q2FImCuODvasZbpUlpoa3FKMR+em1qxkJguemVL1fnC+MeAZGIdPY4xlptVrdD1lmqlAuP6r9crqKDGBJuCFYRICOCJSuM+mvbwdTE9y00xfw6H0DTt43tgNy9T73/bzY/VAPq7g8TVO4PmLLfMPbRzBspr4lfglg6TZOjAryb5+73aZWVoU5Bh65xQAT0a9S5BaC2fmmFDEBTfyY5tGdpamPxhlXgQNPCXiS/T7MoBoX5PH6u3CqYsm0J/ABOkHgQRw+cpAAAAAElFTkSuQmCC)
Find the coordinates of the point which divides the line segment joining the points (-1,7) and (4, -3) in the ratio 2 : 3.
Answer:
Let P(x,y) be the point
P(x,y) = (1,3)
Question 2.
Find the coordinates of the points of trisection of the line segment joining (4,-1) and (-2, -3).
Answer:
points A(4, -1) and B(-2, -3) are shown in the graph above
Now points of trisection means the points which divides the line in three parts. From the figure it is clear that, there will be 2 points which will do that. Let us call them P and Q.
Now clearly point P divides the BA in the ratio 1:2 and point Q divides the line in the ratio 2:1
⇒ Let P and Q be points of trisection
∴ P divides BA internally in ratio 1:2
Such that AP = PQ = QB
Let us apply section formula to the points A and B such that P divides BA in the ratio 1:2⇒ Q divides BA internally in ratio 2:1
Hence, Points of trisection are and
Question 3.
Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6).
Answer:
Let P and Q be line
∴ A divides PQ internally in ratio a:b
⇒ Given that A(-1,6)
6a-3b = -a-b , 10b-8a = 6a + 6b
7a = 2b, 14a = 4b
∴ a:b = 2:7
Question 4.
If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.
Answer:
Let A(1, 2), B(4, y), C(x, 6) and D(3, 5)
If ABCD is a parallelogram
AC and BD bisect each other
⇒ Midpoint of AC
⇒ For AB =
=
⇒ Midpoint of BD
For BD =
=
∴
1 + x = 7 , 8 = 5 + y
x = 6 y = 3
Question 5.
Find the coordinates of point A, where AB is the diameter of a circle whose centre is (2, -3) and B is (1, 4).
Answer:
Let O be the center O(2,-3)
⇒ A(x,y) B(1,4)
∴ O divides AB internally in ratio 1:1
x + 1 = 4
x = 3
y + 4 = -6
y = -10
Question 6.
If A and B are (-2, -2) and (2, -4) respectively. Find the coordinates of P such that and P AB lies on the segment AB.
Answer:
AP = 3/7AB
∴ P divides AB in ratio 3:4
Question 7.
Find the coordinates of points which divide the line segment joining A(-4, 0) and B(0, 6) into four equal parts.
Answer:
⇒ Let x,y and z divide the line into 4 equal parts such that
AX = XY = YZ = ZB
⇒ X divides AB in ration 1:3
⇒ Y divides AB in ratio 1:1
Y(-2,3)
⇒ Z divides AB in ratio 3:1
Question 8.
Find the coordinates of the points which divides the line segment joining A(-2, 2) and B(2, 8) into four equal parts.
Answer:
⇒ Let x,y and z divide the line into 4 equal parts such that
AX = XY = YZ = ZB
⇒ X divides AB in ration 1:3
⇒ Y divides AB in ratio 1:1
Y(0,5)
⇒ Z divides AB in ratio 3:1
Question 9.
Find the coordinates of the point which divides the line segment joining the points (a+b, a-b) and (a-b, a+b) in the ratio 3 : 2 internally.
Answer:
Question 10.
Find the coordinates of centroid of the triangle with vertices following:
(-1, 3), (6, -3) and (-3, 6)
Answer:
The coordinates of centroid are
Question 11.
Find the coordinates of centroid of the triangle with vertices following:
(6, 2), (0, 0) and (4, -7)
Answer:
Question 12.
Find the coordinates of centroid of the triangle with vertices following:
(1, -1), (0, 6) and (-3, 0)
Answer:
Exercise 7.3
Question 1.Find the area of the triangle whose vertices are
(2, 3) (-1, 0), (2, -4)
Answer:Area ΔABC = 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BQCCgEfCHwfzk5J3zHPBHcAAAAAElFTkSuQmCC)
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Question 2.Find the area of the triangle whose vertices are
(-5, -1), (3, -5), (5, 2)
Answer:Area ΔABC = ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= 32
Question 3.Find the area of the triangle whose vertices are
(0, 0) (3, 0) and (0, 2)
Answer:Area ΔABC = ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANQAAAAeCAMAAABjc8D4AAAAAXNSR0IArs4c6QAAAIFQTFRFAAAAAAAAAAA6AABmADpmADqQAGaQAGa2OgAAOgA6OjoAOjo6OjqQOmZmOmaQOma2OpC2OpDbZgAAZgA6ZjoAZrbbZrb/kDoAkGY6kLbbkNv/tmYAtmY6tpBmttv/tv//25A625Bm27Zm27aQ29u22////7Zm/9uQ/9u2//+2///bgC5TRAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACrElEQVRYR+1Ya1PDIBAEn/VZrdVU8RGrpin//wfKHSQccEmIM2rNyIc6bchyu3sch0L8jz+jgH48/jOx5gb6erGcHikhyn9SuRnwy/Mm7ZQurmN59dP5S4fk5eXzL5vBLu9IaHX0gc9TUrq4so+4sTm7G8kqlGi8KjkSWxKlNAMtakiupDxHFxjrhH5bSnnwAI83J/ind+j1aTPdwIFEHiBLFd1G494PlkvB4pjtd10cftTFPmRdhZ/hUPJW1Av7oDyMfNRFbJ7auxd1sQfs3XIEIFUlASDRcBKnYDypCiKopIlOF0ytV/BbCY8ZqxhSfrqTiAIMq+Kj4SUm0VgwnpQCF7YLM3sz69o0yJlJz5QU2oyQgUQOILEqAfDRsBIjfADGkgK/gZT5RJXYgUtBtJGVLKl6hXUykMgBJBkVA5BouiUOwHpIIVgnqRZfRZuKIbVdSHkJeUHRPMCAKpZUbjQAhqSg9pnRZhOBKRs/3BwprXVeDEpKRbO8xW8zACKk8gEYUvE6EVhv+hnWHU6R5M5wyia9Ua+RKNhdQwBN+plo/PvBjoij6S0UJowOUuq4LeRZewq2U4BGAYby1xWKvGhsqoZtUXMYm8qGBYXfmlg5K3xzu4j6KuaYgRmI1kpEAIYrDR4e4fuBUQkYTwoKX5PKzDmFVVgrZDNckTWcuzXu9kYiCjCsio+GlTgF40mJ2vRBWK86OgosCEhq+OwU9Wom5dyeilYit9EzVfHR8K2ArU4ErIOUt5drTIj5Ob0fmc40XYkq/LFof+WaNjqfdhTvxpg5PvzmLj2FH6dKnsQ4a3tzL9bx+dMKkNPs96kbVd/wIpPVpROErItQS32cYtkkkok/cZ9qFy2TG+/XA9+VN9d2S01qlBPkVBlO1dj/Nuy4q3A1kPbON5nxCeB4VmByZgWKAAAAAElFTkSuQmCC)
= ![](data:image/png;base64,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)
= 3
Question 4.Find the value of ‘K’ for which the points are collinear.
(7, -2) (5, 1) (3, K)
Answer:For points to be collinear area of ΔABC = 0
Area ΔABC = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAU8AAAAeCAMAAACbtmwmAAAAAXNSR0IArs4c6QAAAZJQTFRFgYGB////AP//AAD/AAAA///b//+3//+2/9u3/9uR/9uQ29u2/7dm/7Zm27eR27dm27Zm25Fm25E625A6t2YAtmYA///b//+22///2v//2v7/2v7+2//btv//tv7/tv7+tf7/tf7+/9u2/9uQ29u2ttv/tdr+kNv/kNv+kNr/kNr+j9r+/7Zm27aQ27ZmkLbbkLXaZ7b+Zrb/Zrb+ZrX+Zrbb25Bm25A6tpBmZpDbO5DaOpDbOpDaOo/aOpC2OpC1tmc7tmY6OpCQOo+PtmcBtmYBtmYAkGY6kGYBkGYAO2a2O2a1Oma2Oma1O2aQOmaQOmaPZmYAO2ZmOmZmkDs7kDs6OmY6kDo6AWa2AWa1AGa2AGa1kTsBkDsBkDoBkDoAAWaQAGaQZjpmOjqQZzsBOjp8ZjoAOzs6Ojo6OjoAATuQATqQATqPADqQADqPADo6ZwE7ZgE6ZgA6ZwEBZgEBZgEAZgAAOwE6OgE6OgA6OwEBOwEAOgEAOgAAAQFmAQBmAABmAQE6AQA6AAA6AQAAAAAAZZkyuQAAABZ0Uk5TAAEBAQH+/v7+/v7+/v7+/v7+/v7+/hHKkRcAAASOSURBVHja7Vj5d9M4EJZtRLeFAG2oHQJlgcCGlHD1MpBClytc6bIsRyCQFgKUM9yUM6WQ6P/myZZsyZFkJ015vLeeH/raejyf9Hk082kAiC2239rMk5WYhN7Z1NWFmM+emh3zGfMZ8/m/49OcL8RkrMDgnWkd01i8lwrj0zxyf6Tbr3V5T6eC41eCeWQcub9d6+rN5D9/aQyfNkIIFdR8mvMnUl1/tszjsc7o/JVgHp3VmZTWJebAowmdyU9mIwXZDldUCDKfslywsRA6ewgWAY/QOW10jznwYVTrhM/88siKCotdT0XfX0/BovKZWNqhrQAz+WyrJuGziFA9ZSM0xv6/gn/gB5kGamaVySXy4nKG3d+qg4n43IxQfYvdQuMGk563DQCrCNXTmS+oOaorErmFXqQzn1FznxZMUHF+FpvZwBoyjTHnKf7weeUOJV5c4nOxVxtMmJ+bmzkdzjF0gv4vuALCaj2tgcR3BZ3Y6bnjxNJJmBTziRdpc0siC7bxQQzVqkKvYkWyv9UGE/IJ5+pb7AJbLwmHQ992aGDoprqSJpd2aiB5i3caxn87fCLXmC+badwoAcEWceaYZT5jiogaTRKRFyiSmiZyjw7W/roSjH8hx6RO/9cbpTWgnU+cpvD6Xi7JhlteCDclBz5P6PDaKF9uh59v1aT9yA4cM9vtELiy5ethUkboxWwxmC+rCybpR0M/ctzOncR0y2jiWVoLkQK3jMTTdHQ+rdoVsicyyKMFyl4eKeK17V5AqKQ6g47X1BPUPBrKJwXzYgbB2DByMHboGM7n2tqV5e06AIM4tuHnJ+b17Dj+Df4tP/XJpZ1nsNO6BwjNGqF8muWstVhhB3l0i9biqdoIANabg+CAvFMQL7PMeMnrJwHzYwbAuDBSMG7oGF4/y1nrfWUNgOWDxkYnUymffe9O1fAtafC/hdtSPvvenq79qYG+V4e0TbQt+fUzyKdZLACQdy9MpNK7LdcpRwWZauaqXNDLWpT0dxaMeHcL5nUlDkzEJzw7bYD1LVfA93/EfLr93amWRNerutJw67jOCXnQ9/a4pL+b86iZtRbdGyhZoyMJealtFyII8l3nJtX6kwMjMdvBvDBKMI/PMP0J51AzZ71HCDP3x7lJg+pPTter+EzgDu8e/WN6qP4UDJ7oovN0zQdKqgtOhabOy0nxlUVoNGYQzA+jAvP5jATmSfuXDp8ejwlKo5JP+mzTRaP9fuR3FymfTuKWs54ysaV0sl4A7HfPruq8+lglIAbzwqjB6Fojgfm2oTFukPs7vL7X9MSSjE94bdSkYil5yWi/vzPdpe1mQQd5eOSzbb50gaZrCYC8ZIuel/UmS2phpJEPE5MD88OowPy1djJfWvs6p/d/de9JsDqzrTp7nnYheOauWDbB6ux5ouUTFw2QOKwL5kvib+oP8vBI8uECupwiBR8/kG2ReoGphit0Io0kuZgsmBdGDUbX2tn8c7BB9JIz/3RASfXEIl44cYLV1r9p0oMw5oTuzz995uK5fC9N2V1i63hgGNPZS1N0l9g6N1V3ia1j+wkoz4n6zaGWDQAAAABJRU5ErkJggg==)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
∴ 8 - 2k = 0
K = 4
Question 5.Find the value of ‘K’ for which the points are collinear.
(8, 1), (k, -4), (2, -5)
Answer:For points to be collinear area of ΔABC = 0
Area ΔABC = ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
18-6k = 0
K = 3
Question 6.Find the value of ‘K’ for which the points are collinear.
(K, K) (2, 3) and (4, -1).
Answer:For points to be collinear area of ΔABC = 0
Area ΔABC = 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BQCCgEfCHwfzk5J3zHPBHcAAAAAElFTkSuQmCC)
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= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
⇒ K2 -11k-12 = 0
⇒ K(k-12) + (k-12) = 0
⇒ (K-12)(k + 1) = 0
⇒ K = 12 or k = -1
Question 7.Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, -1), (2, 1) and (0, 3). Find the ratio of this area of the area of the given triangle.
Answer:1 sq. unit; 1 : 4
⇒ Let A(0,-1),B(2,1),C(0,3)
So midpoints of AB and BC and CD
⇒ Midpoint formula
![](data:image/png;base64,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)
⇒ For AB = ![](data:image/png;base64,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)
AB = ![](data:image/png;base64,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)
AB = ![](data:image/png;base64,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)
⇒ For BC
BC = ![](data:image/png;base64,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)
BC = ![](data:image/png;base64,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)
BC = ![](data:image/png;base64,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)
⇒ For AC
AC = ![](data:image/png;base64,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)
AC = ![](data:image/png;base64,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)
AC = ![](data:image/png;base64,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)
(1,0)(1,2)(0,1)
Area ΔXYZ = ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKAAAAAeCAMAAACc0eUaAAAAAXNSR0IArs4c6QAAAIdQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6Ojo6OjqQOmZmOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZpDbZrbbZrb/kDoAkGY6kLbbkNv/tmYAtmY6tpBmttv/tv//25A625Bm27Zm27aQ29u22////7Zm/9uQ/9u2//+2///bdrbf/wAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAB/UlEQVRYR+1Xa1PDIBAEH7XVWjXWR6rYiq1NGv7/75O7g4SEtJCJduJM+ZA0JAvL3t5BGTu13gqoj3HvMf5ygK/b+bAJMiZPBHs64N8oqNKH5lLVcvpZ9cnZqqMW/fCGkBJXW5zXJ6jSe3plWn7z2olhTzwRklw3lK4kuHl6dxmrzZzzS+zKr+nN4dbA649tTxReLTifQqyaipnn3ZyfU1wzugv+wnYJ/ZajmqQwSFNUD8+qnhi8SkfbXQrTtRPMZytJZFRK9UfATXIk4kngEfTxVU8MnmVnOkoZTLdHQU2GCOYTRxxEtPjUV7ANb0aMwguYvUi0KiGCuBTbEGbldCx4gKCDLwlSOA7hIcJAUF+7ECzVFA0TdiYYwhNBvCJByGHdauEz662W7azFJSgMmHNX6zLEDt5R0CHYim8SrKltCrUZrgqRTRcIcUgBSCiyQ3uIQ3gb4k4eFOOyuAQ9FCIY8iAzSaLFCnmw9B0WvwzlLZLGdtgxiyPwWNACZYYsZQOLtU8JZBaug6BgHV/1ROEhga0R62qQomox0d6/eAYT2Z0EkwE/Du8kPt7picAz2Hj4DDy1N8Q2cfzTQ9ReWubd7+C/Nd87HHOYp5ni8Y2trWeGeR6MPUTVt6ijPklPuaNOH5xsTRYcbJMD55dpflm3vxpH1bpIoAgPl+APUURFbuD5kuIAAAAASUVORK5CYII=)
= ![](data:image/png;base64,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)
= 1 sq cm
⇒ Let A(0,-1),B(2,1),C(0,3)
⇒ Area ΔABC = ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= 4 sq cm
∴ Ratio of Area of triangles is 1:4
Question 8.Find the area of the quadrilateral whose vertices, taken in order, are (-4, -2), (-3, -5), (3, -2) and (2, 3)
Answer:28 sq. units
⇒ Let A = (-4, -2), B = (-3, -5), C = (3, -2) and D = (2, 3)
We draw Line BD and divide the quadrilateral into 2 triangles
ΔABD and ΔBDC
Area of both triangles
⇒ Area ΔBDC = ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAeCAMAAADEgrRGAAAAAXNSR0IArs4c6QAAAFpQTFRFAAAAAAAAAAA6ADo6OgAAOgA6OjoAOma2OpDbZgAAZgA6ZjoAZpDbZrbbZrb/kDo6kGY6kLbbkNv/tmYA25A625Bm27Zm27aQ29u2/7Zm/9uQ/9u2//+2///bQHBKxAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAeUlEQVQoU52QSRKAIAwEE8V9R3HF/39TiKGEk6Vz6RqSCRCAN6kUo9o0Mc9ugDmS4GjjeyJpCvPoG7LMEWPyjgCLaKnBUpcSdo+gBN/HfHvfxzqG+pj+2b5WiNmT1eW9Q19uh+5syoPy7MVNYQrtZux279RKF/aT5C/0bAVGssIejgAAAABJRU5ErkJggg==)
= 16.5 units
A = (-4, -2), B = (-3, -5), D = (2, 3)
Area ΔABD = ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= 11.5 units
⇒ Total area of quadrilateral = Sum of Area of triangles
= ΔBCD + ΔABD
= 16.5 + 11.5 units
= 28 sq units.
Question 9.Find the area of the triangle formed by the points (8, -5), (-2, -7) and (5, 1) by using Heron’s formula.
Answer:Not possible
Let A = (8,-5) B = (-2,-7) and C = (5,1)
AB = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANQAAAAaCAMAAAD44oLuAAAAAXNSR0IArs4c6QAAAIpQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OjoAOjo6OjpmOjqQOmaQOma2OpC2OpDbZgAAZgA6ZgBmZjoAZjo6ZpDbZrbbZrb/kDoAkDo6kDpmkLbbkNv/tmYAtmY6tpBmttv/tv//25A625Bm27Zm27aQ29u22////7Zm/9uQ/9u2//+2///biO1dXgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACnElEQVRYR+1X21LbMBCVUiAtBUpaKDUXQ1FDsWP9/+9Vu5IVWbvryHE7U5joITORtZdz9qKVUod1YODAwIGBCQwY/U5WgtnePkxg4I0cbc9ewVP7dPa8p8fm/Oeekv9MrDlBTNUXxLbXak9/oNzvK60vCjTMIDBq//WgIpnUbg0O2eqSOGNfnI9HI7m5/qT14jvItR/hWPf1Xq0Xu5OZITDU9XEJse0SegDYCWRSu903yLrmA829Wt+ozYr5EOCbxY1Sa41smN4dD2+7bOWDONiiBCKz7ZKc5cKeHNtaG9rFkrIV5uBw1bBntGQoyNQIJ+o0mcMMKI5AtGxkAlPPUuyRzKFd/Cdz1OwEFUrSg1nnJUVBsQSCbLeiEdwRqUhmZvcR0qURK6GW2WtcesYawrAqQ9oEBSUSaArKEYykCkIvyOyGkpL0jab5i6vYXhCzsHGYmmG6UlASgWIE82i1y8/L2MCQzNyub+h9NtdxtvDOJk0x/wSMuXTpaw5AdSsQ34KiIqCzB5V/3SY6lRvs2FvXwKrAJmdXGfRBYG+UPFtBcPyvUr5f0EUjJbUDSQOr1jMq2A0zkgCqPhm5N7oVBjkUna+pElCCrd5LXg3ZDdYzMjfXeDX4GYkvHeyXjWeEcxeD4wkWO1dxTY10pMx2DR7FSKVkmvMrdNnvsXmGd49FFewy2k1W4fLN79woUNr9Svs50OjKaVP5rpyLYWHiTe4WP1Fg2xBBKRiTju5RPl6COfzSe0q+VAihm2vnVZih6QBz/GrvwnTEzX5ShJh9MVCcDnGimGCwP0rIdJddKClMwL8wpZd5NZPA1Agl0zWQZGKa8RyY+p6aReAAU3jypHtmcbr7nVDG/rRTMwgc+M89TruRd8U0L/+P038AdaA8Dp8Xo54AAAAASUVORK5CYII=)
AB = ![](data:image/png;base64,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)
AB = ![](data:image/png;base64,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)
BC = ![](data:image/png;base64,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)
BC = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAG0AAAAaCAMAAACKASIdAAAAAXNSR0IArs4c6QAAAIRQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OjoAOjo6OjqQOmaQOma2OpC2OpDbZgAAZgA6ZgBmZjoAZjo6ZpDbZrbbZrb/kDoAkDo6kDpmkLbbkNv/tmYAtmY6tpBmttv/tv//25A627Zm27aQ29u22////7Zm/9uQ/9u2//+2///bxfS+PgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAB1UlEQVRIS+1VW1vCMAxdp4gC6hQvU5yXTulc////s03Spl0pA/l4ow+jY+fk5Na0KE7rlIF9MiDFkVfojH5528e3A7HdfH2gBUvXH/MvNiMXnxmb6gI+ZOA/SyGux73R9U3kczd7BlJCb+B/hFMJJ+uC4P3dqmjL0VTr+haMt1dClI92111aUkLv720GCA7K3RSeAGcix6dr9DtY6gzSKMsnoyhAWRqXUzqWjeDwWRLVwSX67VeqpmuoBv00QPTeRnR4IRwY7Cu07uDtsGypGmbDq5E0JTeiv9uEERxDozJRcmXSI6maIooSNpP00oBoTMeyOXgUJsCVEVNxnfJqxffUdAnVGxI6oGP/B2pKONsW3ld2zrBa48dO2KhUaZMikz1J8E10CZYc3GyxxnbxzjcIbLKx6dpy8bmRTmOLYwP3/qnWV5CoBnsa60br9wFOFY4tViNoAg+YW3oSosKcuNYGolwsoYrogO/JABPBw1xmz5spmRlIdLp5OgAX2gHHFp+3oF0GcNbLzxKYXOcrDMfXnxQma/1KgzucJWR3AA+jS/ZuTvKHxFdzjP1tswN8RG7zHcAk00I8w3JXxlaNsHVG7zdZzvgu2fU63FU+wfUVnoyjrz/lFi641WcXSQAAAABJRU5ErkJggg==)
BC = ![](data:image/png;base64,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)
AC = ![](data:image/png;base64,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)
AC = ![](data:image/png;base64,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)
AC = ![](data:image/png;base64,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)
Find the area of the triangle whose vertices are
(2, 3) (-1, 0), (2, -4)
Answer:
Area ΔABC =
=
=
=
Question 2.
Find the area of the triangle whose vertices are
(-5, -1), (3, -5), (5, 2)
Answer:
Area ΔABC =
=
=
=
= 32
Question 3.
Find the area of the triangle whose vertices are
(0, 0) (3, 0) and (0, 2)
Answer:
Area ΔABC =
=
=
=
= 3
Question 4.
Find the value of ‘K’ for which the points are collinear.
(7, -2) (5, 1) (3, K)
Answer:
For points to be collinear area of ΔABC = 0
Area ΔABC =
=
=
=
=
∴ 8 - 2k = 0
K = 4
Question 5.
Find the value of ‘K’ for which the points are collinear.
(8, 1), (k, -4), (2, -5)
Answer:
For points to be collinear area of ΔABC = 0
Area ΔABC =
=
=
=
18-6k = 0
K = 3
Question 6.
Find the value of ‘K’ for which the points are collinear.
(K, K) (2, 3) and (4, -1).
Answer:
For points to be collinear area of ΔABC = 0
Area ΔABC =
=
=
=
=
⇒ K2 -11k-12 = 0
⇒ K(k-12) + (k-12) = 0
⇒ (K-12)(k + 1) = 0
⇒ K = 12 or k = -1
Question 7.
Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, -1), (2, 1) and (0, 3). Find the ratio of this area of the area of the given triangle.
Answer:
1 sq. unit; 1 : 4
⇒ Let A(0,-1),B(2,1),C(0,3)
So midpoints of AB and BC and CD
⇒ Midpoint formula
⇒ For AB =
AB =
AB =
⇒ For BC
BC =
BC =
BC =
⇒ For AC
AC =
AC =
AC =
(1,0)(1,2)(0,1)
Area ΔXYZ =
=
=
=
= 1 sq cm
⇒ Let A(0,-1),B(2,1),C(0,3)
⇒ Area ΔABC =
=
=
=
= 4 sq cm
∴ Ratio of Area of triangles is 1:4
Question 8.
Find the area of the quadrilateral whose vertices, taken in order, are (-4, -2), (-3, -5), (3, -2) and (2, 3)
Answer:
28 sq. units
⇒ Let A = (-4, -2), B = (-3, -5), C = (3, -2) and D = (2, 3)
We draw Line BD and divide the quadrilateral into 2 triangles
ΔABD and ΔBDC
Area of both triangles
⇒ Area ΔBDC =
=
=
=
=
=
= 16.5 units
A = (-4, -2), B = (-3, -5), D = (2, 3)
Area ΔABD =
=
=
=
=
= 11.5 units
⇒ Total area of quadrilateral = Sum of Area of triangles
= ΔBCD + ΔABD
= 16.5 + 11.5 units
= 28 sq units.
Question 9.
Find the area of the triangle formed by the points (8, -5), (-2, -7) and (5, 1) by using Heron’s formula.
Answer:
Not possible
Let A = (8,-5) B = (-2,-7) and C = (5,1)
AB =
AB =
AB =
BC =
BC =
BC =
AC =
AC =
AC =
Exercise 7.4
Question 1.Find the slope of the line passing the two given points
(4, -8) and (5, -2)
Answer:Slope
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAVCAMAAAAQExzYAAAAAXNSR0IArs4c6QAAAF1QTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOma2OpC2OpDbZgAAZjoAZrbbZrb/kDoAkLaQkLbbkNv/tmYAtmY6tv//25A627Zm27aQ29v/2////7Zm/9uQ//+2///bIdq9bgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAcUlEQVQoU2NgGNpAToSdVQqPF6TZOSTx+VCanRdvAMhys+EPIGlGPpgCYUYYYBJCaBJmFuBhZOTA6Ug5fkZOKQYJdi5c9sjxg30oDCKxWgFVIMYsissIYbAU2ATsQIadTYpBHOEVTFUyQE+wCA6OxAIAGmoEUCsRzH4AAAAASUVORK5CYII=)
Question 2.Find the slope of the line passing the two given points
(0, 0) and ![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 3.Find the slope of the line passing the two given points
(2a, 3b) and (a, -b)
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 4.Find the slope of the line passing the two given points
(a, 0) and (0, b)
Answer:![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAE4AAAAoCAMAAABn2TxoAAAAAXNSR0IArs4c6QAAAHJQTFRFAAAAAAAAAAA6AABmADqQAGaQAGa2OgAAOgA6OmY6OmZmOmaQOma2OpCQOpDbZgAAZgA6ZjoAZjpmZmYAZrb/kDoAkDo6kGYAkLbbkNv/tmYAtmY6tv//25A625Bm27Zm29u22////7Zm/9uQ//+2///buXs1kQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABe0lEQVRIS+2W607DMAyFHSgbl0HZWLgEyta0ef9XxGmTrNDENtKYQCI/pkn9dOpb4wNwguO0UlXbLdXZC/U2IQbgdNUCWFpNjAE052/4s+AqIcSgW27BPX5N1ah4Qtx5bB6E0wuwPmH6CLEhW7NFrf1aqVVZM2LgXsnK9PXtBsvX3z/DjuhIwOD9ek0X2qi7EFR3SYxLwpi+Wd/b4TRRN5dzwji5GPyOKB3OZsQIORyRNCVNWW2KUUPq9OopvNWimvUtzpwJBs5cFMcKP8ab8WFf+8EtykUMGo9RNeYm+E8+n33WP5BFujm+9+f4kZwi2eNH/a/4OyqA01O1eEsUrpIYpBADMLhunGbUxNjgKsgdMQYoxABtwNX8Vp9/QVks17CG8zthzcmwfvMwbEbGBUSMcQG4pPoatw/jAiLGuABncI3YsEvKLmCKUXtWo+/0S2zYTcUO48I7YLwZHItNu4DURaEc4QI+DYRMjnIBUznKBRw40gVM5IIL+ADOxRwe1r4CSAAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 5.Find the slope of the line passing the two given points
A(-1.4, -3.7), B(-2.4, 1.3)
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAC4AAAAVCAMAAAAO2ixrAAAAAXNSR0IArs4c6QAAAEtQTFRFAAAAAAAAAAA6AABmADpmAGa2OgAAOjpmOmaQOpDbZgAAZjo6ZrbbZrb/kDoAkDo6kNv/tmYAttv/tv//25Bm/9uQ/9u2//+2///bgVTi6AAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAa0lEQVQ4T+WQOQ6AMAwEEw5zBwzY8P+X4kQ0FKCtEBJbJM1o5Vnn/pF1Aj2FvCXD8QEsTpjQSzhHi5R7FaGKfPFgei3Zx95pgJc5fRv7kWMSvrUluCbHXqH4ImE7W0O+IKwx2tlw9QzSH8UOoXMDQzJSxWQAAAAASUVORK5CYII=)
Question 6.Find the slope of the line passing the two given points
A(3, -2), B(-6, -2)
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
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Question 7.Find the slope of the line passing the two given points
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMsAAAA7CAYAAADVaX4qAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAlqSURBVHja7Z2/bxQ5FMe9QUrDr5KDi1eiuCN0ZJyIkgZtJhCQUqyS3dEKCXRbrFYjQZC2yMGGLncJ1NdBaA5SXHcNgeoaSPr7Bam4hh9/AiE39sxmdyczs54ffvZmHOlVSeQ3/szXfn7286AHDx4gbdq0DTbdCdq0abFo0zbEYnF+CtRy1cFD8Mx55JLkucEc20BoxLbMK6Zp3ayvrBzLA4yVlfoxyzRvmpZ9BaGNERV9zCOXpGxAHGvVyycsgtemLHs+j9O3bU3NY2KtleutEyr5lXcu1Jox2IAAqRL8kNSWr6oy7Tp2BKE90LBjuUauYlJ9CN3uMHCRzbm9zyZ6hhHuNAWCzcYdFTqw0SiTUoncxxj9g0vNRWgfGia+47R7V/b6QCUuqnDusgkXl1DH2xVyDeOZZyrEwnRkR8Xin8Ui+svp0D0ZYqFx8gzGz0ilfU1mX6jEJfNnS8jZY/NrFBtx03yrfnwa4+fm4vIFlTpz2SKzssTC2l80L2A8/bzeah2XEn4pykUFzoPYCB29ELGeHIZOzNosgp7Iml1U5aIK5yg2wsINcwy9VHHxqIJYWEg4Zr6Enl1U5qIKZ8qmEMJGzOhlmxMYGVu1dvu0FktA/7RrpwnCb0y7PQHaLuNC3qjIRRXOHTaXG0sGjFgUnupVEIusUCwvIVhazmFshDhaJWidWMuzWiwD/CDVdcg2VeaiEucwNmLiYpptAQ4xhk0sLCTC5nOo9K3qXFTiHMZGSDxuIGNT1bhYGbEA95PqXJQSS0hfabFosWixhPVVq3VGrFiAw4sUnXhXph/QYZHqXFTiHMYmN1A6B+vuVSau005ExsJTGQcqtVjU55xYLLTeIU4tBhQUxPyincBsoH/0KEMRoQ/O337ptbSHCeP6kUYsG/1thVgwKwgu5Ui/ykfS9Cvv4dMsOCcWS9VAT9GY+Yq3kz0oG6Kg0E5bapS/Jxi93u8MbGyVG61z0CNYGj88IBu8YqF/P43RC6+tr07ze/4XolAs/o2NhUe1Wutb/8slmkurVTtjILTDRvNAI+941kvU71ajfM7AaGv/f/HEdmm+MQt1WrsjFv/GJGcH4M9BO5qBYrkxPjc6ep52zCkRD7LUuGxMTpo/d6C37cp37gtr7PgXZCLN9WPmp6R+OIvIU+dHR9+N32jPxV58sheJ7PS+fMu2/U2V4FUnBtn1eBFILmzDk7XdL2AmYipuzs1Qp1+dbix8OvD/jmgmKveuAyVDAtlE/lOzhGntxW4hxkJJJBSmeGL+6B8d3WMc6DPUhhvzY8pcSuNHUrF0znf5xdIx28R32GhMzzf1+CdaLLTi0rRuz6QJN92/LWxis3K/dxCiM6orGAIyIMYWiwul8HKqVrtFEHrHG4p5UN6KghI2ytPRSPYBwTh+eEDeZi2WjmD9vxfJhc52lUrwkX/WJ5y1M3S9MWU2bwWLCG3SGRMiIRLGJhq895D0rAxvKAaZdfEyHyMVMrKOSPWx5AxMLD+SZsOixEL92M8CYXOzb2aRlA2j0Qk27dQVmfSoDu+6R1SmMtK5zkN2ctbIqD5VRSw0M0TLR52hfBuR0m+yLoNI6kd6sRg7Zdse6804NSuk6sxszqyCP/pnNxliySo9vv/MQANiLLG4C/vubq83tX/iWbxCQPFlhnbZ5pOx8KjeWgGvD0nqR3qxHMyGuT4YO3Rx708hyxBLnBBscHhLXkOdPoglFraw39/MQUfq9fLJ0hh6RV+GQcfK40DZ27+Bg8cObirRh2LXDCH0UeaufBI/sg7DDvjgiLY31QrJJcsQjPpSIXgNcj3KLRZWo+0s7INHrcGhWBwoDTdz84XHojaVWO00m/n6XyB+4F1L08lhfkCtWfp96B/YoLlkEYJRsTuCWxy0oZg1Y26xsHy5b3EYJxSTtZB0kxAHxPIlronwA1Is3cWwM7D11GRAc0kbglGh0LVyUHYs4G8zZcwlFvc+KbQeNOV103fRoZjMrEuQyKGN1w+hYqGnLiSLJU0I5p6OuGwQYt0L+J3wa3C5xOLunobXznezYmw9U5AhlnLAWSF6u6K7mZXtpXHds1gH4/K0foQBiWpzkFjYUZFW+Vv31EXha68fkGIZNBBEPWMn/e2tufrCp8X63Dgh5qroZxgoFmcRf4It4ln6s37SLwZP7cTd8KKzS7MadGhPJBR2pIRukGJju9xoEC/5wO7rxaS6mnmHsZcSfyal5g9Z+xEEJKrNzktm2+UxlqZ2wuG5+uJ478vUmC/NemeqdhGefiFrn4WFYMRa4+jX+oE1Ckt/u+9YkGWxZ5NKLG6xC/q3G9cVP/gvYWPX9/jjv4C8t8gDe/QhSpPFX3p9KBYnfw86ZpFamE6fdNLCBd9mWBZ+BB2kHNRmT5o6fMGN8R/0ou/ANafAg5S+NdPjsOxV1DPSbF708znvJcAOfqKDlIleMsFnkKCNjnYWIe2sc/xRZ8NEtKkaF1H9KpKNFssAoHRE5snIZAZEUJsqcRHZr1os2YLiKirqfuwm+xAvDIjINlXhIrpf4zDWYokYzbyiou1uUZEBWlTEG4YJae+QhcdRjCdSFo7lXiwqFBVpsYAw/piWca7FwlVUBLzQ1GKRwJizcCzXYoksKvJy/uCXdGuxwDGOWTgGJxb74qWjCP83226fHYZOhiwq6gcyexajo+8v2u1LIO25XN4PCxeZjMPYiBgxh+bmQ+iiIpn9lLcbKdMwBru+dZguoPaKiqR8r8Q9lasvBgdiHKtwLIyNEAdlfgaO1/a8L/bKuuSC1mlAfytlGLhkzThJ4VgYGzGLLQnfHoljvEVFouNo6G+lqM5FFcZhbAQtJumhPXlf5B3UibTATeZRC/eOA7wl5TN5inLJmjFv4VgQm4kQNgLjY7Sp2pTfLSqq3A/43QjYSxtSjQqzblGPixjGyQrHotiIm/Jr5OqIM+XLOEoS1omyi4o6flTJyLqstZJqXFRijNgaJ5yN0FFsBuNnvHckC49fFSgq6mZa0l8PdBi4qMZ4EBvhoxhLwQHf5+U3rqKixeDrRzN9UVv14zR9K/uaWVW4ZGnNlIVj9FYjOohEsQHI+uBV+qmywzjtJ8rOZFz+rLnAsQGZ9ikYuqjMKxg3RJiqUBiqfHlLc+mycSKPBR42oGCmLHshb2DiwJAlmDxyScIG1LnbljljmtbNvHwEFKIqUHOBY5PrWFWbtlgzke4Ebdq0WLRpy9T+BzMxC9lX/2HlAAAAAElFTkSuQmCC)
Answer:![](data:image/png;base64,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)
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Question 8.Find the slope of the line passing the two given points
A(0, 4), B(4, 0)
Answer:![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAE4AAAAoCAMAAABn2TxoAAAAAXNSR0IArs4c6QAAAHJQTFRFAAAAAAAAAAA6AABmADqQAGaQAGa2OgAAOgA6OmY6OmZmOmaQOma2OpCQOpDbZgAAZgA6ZjoAZjpmZmYAZrb/kDoAkDo6kGYAkLbbkNv/tmYAtmY6tv//25A625Bm27Zm29u22////7Zm/9uQ//+2///buXs1kQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABe0lEQVRIS+2W607DMAyFHSgbl0HZWLgEyta0ef9XxGmTrNDENtKYQCI/pkn9dOpb4wNwguO0UlXbLdXZC/U2IQbgdNUCWFpNjAE052/4s+AqIcSgW27BPX5N1ah4Qtx5bB6E0wuwPmH6CLEhW7NFrf1aqVVZM2LgXsnK9PXtBsvX3z/DjuhIwOD9ek0X2qi7EFR3SYxLwpi+Wd/b4TRRN5dzwji5GPyOKB3OZsQIORyRNCVNWW2KUUPq9OopvNWimvUtzpwJBs5cFMcKP8ab8WFf+8EtykUMGo9RNeYm+E8+n33WP5BFujm+9+f4kZwi2eNH/a/4OyqA01O1eEsUrpIYpBADMLhunGbUxNjgKsgdMQYoxABtwNX8Vp9/QVks17CG8zthzcmwfvMwbEbGBUSMcQG4pPoatw/jAiLGuABncI3YsEvKLmCKUXtWo+/0S2zYTcUO48I7YLwZHItNu4DURaEc4QI+DYRMjnIBUznKBRw40gVM5IIL+ADOxRwe1r4CSAAAAABJRU5ErkJggg==)
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Find the slope of the line passing the two given points
(4, -8) and (5, -2)
Answer:
Slope
Question 2.
Find the slope of the line passing the two given points
(0, 0) and
Answer:
Question 3.
Find the slope of the line passing the two given points
(2a, 3b) and (a, -b)
Answer:
Question 4.
Find the slope of the line passing the two given points
(a, 0) and (0, b)
Answer:
Question 5.
Find the slope of the line passing the two given points
A(-1.4, -3.7), B(-2.4, 1.3)
Answer:
Question 6.
Find the slope of the line passing the two given points
A(3, -2), B(-6, -2)
Answer:
Question 7.
Find the slope of the line passing the two given points
Answer:
Question 8.
Find the slope of the line passing the two given points
A(0, 4), B(4, 0)
Answer: