Coordinate Geometry-Important Questions

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

2.   Find the distance between the points (-8/5, 2) and (2/5, 2).

3.   In triangle ABC, D and E are mid-points of the sides BC and AC respectively. Find the length of DE. Prove that DE = 1/2AB.

4.   Points P (5, -3) is one of the two points of trisection of the line segment joining points A(7, -2) and B(1, -5) near to A. find the coordinates of the other point of trisection.

5.   Find the area of quadrilateral ABCD whose vertices are A (1, 0), B (5, 3), C (2, 7), D ( -2, 4).

6.   Points P, Q, R and S divide a line segment joining A (2, 6) and B (7, -4) in five equal parts. Find the coordinates of P and R.

7.   Find the relation between x and y if points (2, 1), (x, y) and (7, 5) are collinear.

8.   If A (-2, 4), B (0, 0) and C (4, 2) are the vertices of triangle ABC, then find the length of the median through the vertex A.

9.   If points A (4, 3) and B (x, 5) are on the circle with centre O (2, 3), find the value of x.

10.   If vertices of a triangles are (1, k), (4, -3) and (-9, 7) and its area is 15 sq. units then find then the value of k.

11.   Find the area of triangle ABC whose vertices are A (-5, 7), B (-4, -5) and C (4, 5).

12.   If point A (0,2) is equidistant from the point B (3, p)and C (p, 5), find p.