# Class 10 – Coordinate Geometry – Important Questions

Coordinate Geometry – Important Questions

1. Find a relation between x and y such that the point (x , y) is equidistant from the points (7, 1) and (3, 5).
2. Find the distance between the following pairs of points :
1. (2, 3), (4, 1)
2. (-6, 2), (-4, -3)
3. (7, 6), (2, 1)
4. (4, -3), (2, -8)
5. (a, b), (– a, – b)
3. Check whether (7, – 4), (7, 5) and (6, – 1) are the vertices of an isosceles triangle.
4. Find the ratio in which the point P (3/4, 5/12) divides the line segment joining the points A (1/2, 3/2) and B (2, -5).
5. Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
1. (– 1, – 2), (1, 0), (– 1, 2), (– 3, 0)
2. (–3, 5), (3, 1), (0, 3), (–1, – 4)
6. If the points (x,y) is equidistant from the points (a+b, b-a) and (a-b, a+b), prove that bx = ay.
7. Find the relation between x and y if points (2, 1), (x, y) and (7, 5) are collinear.
8. Find the value of x for which the distance between the points P (4, -5) and Is 10 units.
9. Find the ratio in which point (x, 2) divides the line segment joining points (-3, -4) and (3, 5). Also find the value of x.
10. Find the value of k if the points A(2, 3), B(4, k) and C(6, –3) are collinear.
11. 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 to the area of the given triangle.
12. If the points A (1, –2), B (2, 3) C (a, 2) and D (– 4, –3) form a parallelogram, find the value of a and height of the parallelogram taking AB as the base.
13. Find the point of y-axis which is equidistant from the points (-5, -2) and (3, 2).
14. Find the coordinates of the points which divides the line segment joining the points (-2,0) and (0,8) in four equal parts.
15. Point P (5, -3) is one of the two points of trisection of the line segment joining the points A (7, -2) and B (1, -5) near to A. Find the coordinates of the other point of trisection.
16. Show that the point P (-4, 2) lies on the line segment joining the points A (-4 , 6) and B (-4, -6).
17. If A (-2, 4) ,B (0, 0) , C (4, 2) are the vertices of a ∆ABC, then find the length of median through the vertex A.
18. Find the coordinates of a point A, where AB is diameter of a circle whose centre is (2, -3) and B is (1, 4).
19. If the point A(1,2), B(0,0) and C(a,b)are collinear, then find the relation between a and b.
20. Find k so that the point P(-4,6) lies on the line segment joining A (k,0) and B (3, -8). Also find the ratio in which P divides AB.
21. Two opposite vertices of a square are (-1,2) and (3, 2). Find the coordinates of the other two vertices.
22. If the points (x,y) ,(-5,-2) and (3,-5) are collinear, then prove that 3x+8y+31 = 0.
23. Find the ratio in which the Y-axis divides the line segment joining the points (5, -6) and (-1, -4). Also find the coordinates of the point of division.
24. Find the centre of a circle passing through the points (6,-6), (3, 7) and (3, 3).
25. Points P, Q , R, and S in that order are dividing a line segment joining A (2, 6) and B (7, -4) in five equal parts. Find the coordinates of point P and R ?