Coordinate Geometry Class 10 Practice Questions

CSCE TUTORIAL

Coordinate Geometry

Class – X                                                                                                                                                                            Mathematics

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 a point on the y-axis equidistant from (-5, 2) and (9, -2)

3. Find the distance of the point (-3, 4) from the x-axis.

4. Find the distance of the point P (2, 3) from the x-axis.

5. Find the coordinates of the points of trisection (i.e., points dividing into three equal parts) of the line segment joining the points A(2, – 2) and B(– 7, 4).

6. Find the value of a when the distance between the points (3, a) and (4, 1) is √10.

7. Find the value of x, y if the distances of the point (x, y) from (- 3, 0) as well as from (3, 0) are 4.

8. If the points (2, 1) and (1, -2) are equidistant from the point (x, y), show that

x + 3y = 0.

9. Which point on the x-axis is equidistant from (5, 9) and (-4, 6)?

10. Find a point on the x-axis which is equidistant from the points (7, 6) and (-3, 4).

11. The length of a line segment is of 10 units, and the coordinates of one end-point are (2, -3). If the abscissa of the other end is 10, find the ordinate of the other end.

12. Show that the points A(- 4, -1), B(-2, – 4), C(4, 0) and D(2, 3) are the vertices points of a rectangle.

13. The points A (2, 9), B (a, 5) and C (5, 5) are the vertices of a triangle ABC, right-angled at B. Find the values of a and hence the area of triangle ABC.

14. Prove that the points (-2, 5), (0, 1) and (2, -3) are collinear.

15. The coordinates of point P are (-3, 2). Find the coordinates of the point Q, which lies on the line joining P and origin such that OP = OQ.

16. The three vertices of a parallelogram are (3, 4), (3, 8) and (9, 8). Find the fourth vertex.

17. Find a point which is equidistant from points A (-5, 4) and B (-1, 6). How many such points are there?

18. The centre of a circle is (2a, a – 7). Find the values of a if the circle passes through the point (11, -9) and has diameter 10√2 units.

19. Ayush starts walking from his house to the office. Instead of going to the office directly, he goes to the bank first, from there to his daughter’s school and then reaches the office. What is the extra distance travelled by Ayush in reaching the office? (Assume that all distances covered are in straight lines). If the house is situated at (2, 4), bank at (5, 8), school at (13, 14) and office at (13, 26) and coordinates are in kilometers.

20. Find the ratio in which the line segment joining the points (– 3, 10) and (6, – 8) is divided by (– 1, 6).

21. Find the coordinates of point A, where AB is the diameter of the circle whose centre is (2, -3) and B is (1, 4).

22. If (a, b) is the mid-point of the line segment joining the points A (10, -6), B(k, 4) and a – 2b = 18, find the value of k and the distance AB.

23. If P(9a – 2, -b) divides the line segment joining A(3a + 1, -3) and B(8a, 5) in the ratio 3 : 1, find the values of a and b.

24. If the points (-2, 1), (1, 0), (x, 3) and (1, y) form a parallelogram, find the values of x and y.