Practice Set 5.2
- Find the coordinates of point P if P divides the line segment joining the points…
- In each of the following examples find the co-ordinates of point A which divides…
- Find the ratio in which point T(-1, 6)divides the line segment joining the pointsP(-3,…
- Point P is the centre of the circle and AB is a diameter. Find the coordinates of point…
- Find the ratio in which point P(k, 7) divides the segment joining A(8, 9) andB(1, 2).…
- Find the coordinates of midpoint of the segment joining the points (22,20) and (0, 16).…
- Find the centroids of the triangles whose vertices are given below. (1) (-7, 6), (2,…
- In ΔABC, G (-4, -7) is the centroid. If A (-14, -19) and B(3, 5) then find…
- A(h, -6), B(2, 3) and C(-6, k) are the co-ordinates of vertices of a triangle whose…
- Find the co-ordinates of the points of trisection of the line segment AB with A(2, 7)…
- If A (-14, -10), B(6, -2) is given, find the coordinates of the points which divide…
- If A (20, 10), B(0, 20) are given, find the coordinates of the points which divide…
Practice Set 5.2
Find the coordinates of point P if P divides the line segment joining the points A(-1,7) and B(4,-3) in the ratio 2:3.
Answer:
A point P(x,y) divides the line formed by points (a,b) and (c,d) in the ratio of m:n, then the coordinates of the point P is given by
and 
In the given question 
x = 
= 1
y = 
y = 3
Hence the coordinates of the point are (1,3).
Question 2.
In each of the following examples find the co-ordinates of point A which divides segment PQ in the ratio a:b.
(1) P(-3, 7), Q(1, -4), a:b = 2:1
(2) P(-2, -5), Q(4, 3), a:b = 3:4
(3) P(2, 6), Q(-4, 1), a:b = 1:2
Answer:
A point P(x,y) divides the line formed by points (a,b) and (c,d) in the ratio of m:n, then the coordinates of the point P is given by
and
Where m and n is defined as the ratio in which the line segments are divided
1. x = 
x = 
y = 
y = 
2. x = 
X = 
y = 
y = 
3. x = 
= 0
y = 
y = 
Question 3.
Find the ratio in which point T(-1, 6)divides the line segment joining the pointsP(-3, 10) and Q(6, -8).
Answer:
A point P(x,y) divides the line formed by points (a,b) and (c,d) in the ratio of m:n, then the coordinates of the point P is given by
and
In the given question,
Let the point T divide the line PQ in the ratio m:n
Here x = -1 and y = 6
...(1)
.... (2)
Simplifying (1) we get,
-m-n = -3n + 6m
2n = 7m
Simplifying (2) we get,
6m + 6n = 10n-8m
14m = 4n
From both we get 
Hence the point T divides PQ in the ratio 2:7
Question 4.
Point P is the centre of the circle and AB is a diameter. Find the coordinates ofpoint B if coordinates of point A and P are (2, -3) and (-2, 0) respectively.
Answer:
According to the mid point theorem the coordinates of the point P(x,y) dividing the line formed by A(a,b) and B(c,d) is given by:
In the given question A = (1,-3) and midpoint P is (-2,0).
Let coordinates of B be (c,d)
Then,
And
Solving for c and d, we get
-4 = 2 + c
c = -6
d = 3
Hence the coordinates of point B are (-6,3).
Question 5.
Find the ratio in which point P(k, 7) divides the segment joining A(8, 9) andB(1, 2). Also find k.
Answer:
A point P(x,y) divides the line formed by points (a,b) and (c,d) in the ratio of m:n, then the coordinates of the point P is given by
and
In the given question,
Let the point P divide AB is the ratio 1:k
Y coordinate of P
Simplifying
7k + 7 = 9k + 2
2k = 5
k = 
and the ratio = 1:
= 
Therefore point P divides AB in the ratio 2:5
Question 6.
Find the coordinates of midpoint of the segment joining the points (22,20) and (0, 16).
Answer:
According to the mid point theorem the coordinates of the point P(x,y) dividing the line formed by A(a,b) and B(c,d) is given by:
The coordinates of midpoint(x,y) are
Hence the coordinates are (11,18)
Question 7.
Find the centroids of the triangles whose vertices are given below.
(1) (-7, 6), (2, -2), (8, 5)
(2) (3, -5), (4, 3), (11, -4)
(3) (4, 7), (8, 4), (7, 11)
Answer:
The coordinates of the centroid (x,y) od a triangle formed by points (a,b), (c,d), (e,f) is given by
1. 
2. 
3. 
Question 8.
In ΔABC, G (-4, -7) is the centroid. If A (-14, -19) and B(3, 5) then find theco-ordinates of C.
Answer:
The coordinates of the centroid (x,y) od a triangle formed by points (a,b), (c,d), (e,f) is given by
In the given question (x,y) = (-4,-7)
Hence 
Solving for e, we get
e = -1
Solving for f, we get
f = -7
Hence the coordinates of the third point are (-1,-7)
Question 9.
A(h, -6), B(2, 3) and C(-6, k) are the co-ordinates of vertices of a trianglewhose centroid is G (1, 5). Find h and k.
Answer:
The coordinates of the centroid (x,y) od a triangle formed by points (a,b), (c,d), (e,f) is given by
In the given question:
Solving for h we get
h = 7
Solving for k we get
k = 18
Question 10.
Find the co-ordinates of the points of trisection of the line segment AB with A(2, 7) and B(-4, -8).
Answer:
let The points of trisection of a given line AB be P and Q
Then the ratio AP:PQ:QB = 1:1:1
Hence we get AP:PB = 1:2
And AQ:QB = 2:1
A point P(x,y) divides the line formed by points (a,b) and (c,d) in the ratio of m:n, then the coordinates of the point P is given by
and
To find point P(x,y)
x = 0
y = 2
To find the point Q(x',y')
x' = -2
y' = -3
Hence point P = (0,2) and Q = (-2,-3)
Question 11.
If A (-14, -10), B(6, -2) is given, find the coordinates of the points whichdivide segment AB into four equal parts.
Answer:
let the points dividing AB be C,D,E.
AC:CD:DE:EB∷1:1:1:1
A point P(x,y) divides the line formed by points (a,b) and (c,d) in the ratio of m:n, then the coordinates of the point P is given by
and
For C m:n ∷ 1:3
For D m:n ∷2:2
For E m:n ∷ 3:1
Hence coordinates of C = (-9,-8)
D = (-4,-6)
E = (1,-4)
Question 12.
If A (20, 10), B(0, 20) are given, find the coordinates of the points which divide segment AB into five congruent parts.
Answer:
Let the points dividing AB be C,D,E,F
AC:CD:DE:EF:FB∷1:1:1:1:1
A point P(x,y) divides the line formed by points (a,b) and (c,d) in the ratio of m:n, then the coordinates of the point P is given by
and
For C m:n ∷ 1:4
For D m:n ∷ 2:3
For E m:n ∷ 3:2
= 8
For F m:n ∷ 4:1
