Test 07 || Class 10th Maths || Ch. 07 Co-ordinate Geometry (SIQ) 2

Some important sums of 

7. Co-ordinate Geometry

1. Find the value of x if the distance between the points (x, - 1) and (3, 2) is 5.

2. Find the co-ordinate of A (x, y) is equals to (3,-5) is equal to (- 7, 4) and centroid G (2, - 1).

3. If the point P(x, y) is equidistance from the point A (5, 1) and B (- 1, 5) prove that 3x= 2y.

4 If the point (x, y) is equidistant from the point (a + b, b - a) and (a - b, a + b) prove that bx = a y.

5. If the distance of P ( x, y)  from the points A (3, 6) and B( - 3, 4) are equal, prove that 3x + y = 25.

6. If A(4, - 8) B (3, 6) and C (5, - 4) are the vertices of a triangle ABC, D is the midpoint of BC and P is a point on a line such that AP /PD =  2, find the coordinates of P.

7. The coordinates of the midpoint of the line joining the points to (2p + 2, 3) and (4, 2q + 1) are (2p, 2q). Find the values of p and q.

8. A ( - 4, - 2), B (- 3, - 5) , C(3, - 2) and D (2, k) are the vertices of the quadrilateral ABCD. Find the value of k if the area of the quadrilateral is 28 square units.

9. The coordinates of the vertices of triangle ABC are A (4, 1),  B (- 3, 2) and C (0, k). Given that the area of triangle ABC is 12 unit square, find the value of k.

10. Prove that the area of the triangle whose vertices are (t, t - 2), (t + 2, t + 2) and (t + 3, t) is independent of t .

11. The coordinates of the midpoint of the line joining the points to (2p + 1, 4) and (5, q - 1) are (2p, q). Find the values of p and q.

12. Three consecutive vertex of the parallelogram ABCD are A (1, 2,), B (1, 0) and C (4, 0) then find the coordinates of the fourth vertex D

13. The line segment joining the points P (3, 3) and Q (6, - 6) is trisected at the point A and B such that A is nearer to P. If A lies on the line given by 2x + y + 1=0, find the value of k.

14. If P (x, - y) is any point on the line joining joining the point A (a, 0) and B (0, b) then show that x/a + y/b = 1.

15. Determine the ratio in which the line 3x + 4y - 9 = 0 divides the line segment joining the points (1, 3) and (2, 7).

16. Let the opposite angular points of a square be (3, 4) and (1, - 1), find the coordinates of the remaining angular points.

17. The midpoints of the sides of the triangle are (3, 4), (4, 1) and (2, 0), find the coordinates of the vertex of the triangle.

18. If two vertices of an equilateral triangles are (0, 0) and (3, root 3), find the third vertex.

19. If the coordinates of the midpoints of the sides of a triangle are (1, 1), (2, - 3) and (3, 4), find its centroid.

20. Find the coordinates of the point equidistant from the points A (1, 2),  B (3, - 4) and C (5, - 6).