### Co-ordinate Geometry Class 9th Mathematics AP Board Solution

##### Question 1.Plot the following points in the Cartesian plane whose x, y co-ordinates are given. Answer:  Question 2.Are the positions of (5, -8) and (-8, 5) is same? Justify your answer.Answer: No, positions of (5, -8) and (-8, 5) is not same because (5, -8) lies in IV quadrant and (-8, 5) lies in II quadrant.Question 3.What can you say about the position of the points (1, 2), (1, 3), (1, -4), (1, 0), and(1, 8). Locate on a graph sheet.Answer:From the given points (1, 2), (1, 3), (1, -4), (1, 0), and(1, 8), we can say that all these points lie on a line parallel to Y-axis at a distance of 1 unit. Question 4.What can you say about the position of the points (5, 4), (8, 4), (3, 4), (0, 4),(-4, 4), (-2, 4)? Locate the points on a graph sheet and justify your answer.Answer:From the given points (5, 4), (8, 4), (3, 4), (0, 4),(-4, 4), (-2, 4), we can say that all these points lie on a line parallel to X-axis at a distance of 4 units. Question 5.Plot the points (0, 0),(0, 3), (3, 4), (4, 0) in graph sheet. Join the points with straight lines to make a rectangle. Find the area of the rectangle.Answer:Plotting the points : Joining the lines to form a rectangle and finding its area : Finding the area :From the graph, we can see that,L = AD = 4 unitsB = ED = 3 unitsNow, area of rectangle = L × B = 4 × 3 = 12 sq. unit.∴ Area of rectangle BEDA = 12 sq. unit.Question 6.Plot the points (2, 3), (6, 3) and (4, 7) in a graph sheet. Join them to make it a triangle. Find the area of the triangle.Answer:Plotting the points : Joining the points to form a triangle and finding its area : Finding the area :From the graph, we can see that,H = 4 unitsB = AB = 4 unitsArea of the triangle = × B × H= × 4 × 4 = 8 sq. unit.∴ Area of triangle CAB = 8 sq. unit.Question 7.Plot at least six points in a graph sheet, each having the sum of its coordinates equal to 5. {Hint : ( -2, 7) (1, 4) .............}Answer:The points whose sum of co-ordinates is equal to 5 are :(2,3), (3,2), (0,5), (5,0), (1,4), (4,1). Question 8.Look at the graph. Write the coordinates of the points A, B, C, D, E, F, G, H, I, J, K, L,L, M, N, P, O and Q. Answer:From the graph, we can see that co-ordinates of the given points are :Co-ordinates of point A are : (-3,4)Co-ordinates of point B are : (0,5)Co-ordinates of point C are : (3,4)Co-ordinates of point D are : (2,4)Co-ordinates of point E are : (2,0)Co-ordinates of point F are : (3,0)Co-ordinates of point G are : (3,-1)Co-ordinates of point H are : (0,-1)Co-ordinates of point I are : (-3,-1)Co-ordinates of point J are : (-3,0)Co-ordinates of point K are : (-2,0)Co-ordinates of point L are : (-2,4)Co-ordinates of point M are : (-1,0)Co-ordinates of point N are : (-1,3)Co-ordinates of point O are : (0,0)Co-ordinates of point P are : (1,3)Co-ordinates of point Q are : (1,0)Question 9.In a graph Sheet Plot each pair of points, join them by line segmentsi. (2, 5), (4, 7)ii. (-3, 5), (-1, 7)iii. (-3, -4), (2, -4)iv. (-3, -5), (2, -5)v. (4, -2), (4, -3)vi. (-2, 4), (-2, 3)vii. (-2, 1), (-2, 0)Now join the following pairs of points by straight line segments, in the same graph.viii. (-3, 5), (-3, 4)ix. (2, 5), (2, -4)x. (2, -4), (4, -2)xi. (2, -4), (4, -3)xii. (4, -2), (4, 7)xiii. (4, 7), (-1, 7)xiv. (-3, 2), (2, 2)Now you will get a surprise figure.What is it?Answer:Plotting the first set of points and forming their line segments :i. (2, 5), (4, 7) → A,Bii. (-3, 5), (-1, 7) → C,Diii. (-3, -4), (2, -4) → E,Fiv. (-3, -5), (2, -5) → G,Hv. (4, -2), (4, -3) → I,Jvi. (-2, 4), (-2, 3) → K,Lvii. (-2, 1), (-2, 0) → M,N Plotting the second set of points and forming their line segments :viii. (-3, 5), (-3, 4) → O,Pix. (2, 5), (2, -4) → Q,Rx. (2, -4), (4, -2) →S,Txi. (2, -4), (4, -3) → U,Vxii. (4, -2), (4, 7) → W,Xxiii. (4, 7), (-1, 7) →Y,Zxiv. (-3, 2), (2, 2) → A1,B1 PDF FILE TO YOUR EMAIL IMMEDIATELY PURCHASE NOTES & PAPER SOLUTION. @ Rs. 50/- each (GST extra)

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