Coordinate Geometry-Sample Papers

1.   For what value of p, the points (-5, 1), (1, p) and (4, -2) are collinear? (2)

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

3.   If point P (x, y) is equidistant from the points A (3, 6) and B (-3, 4), prove that 3x + y . 5 = 0. (3)

4.   The coordinates of A and B are (1, 2) and (2, 3). If P lies on AB then find the coordinates of P such that: AP/PB = 4/3. (3)

5.   Show that the triangle PQR formed by the points P (√2, √2), Q (-√2, -√2) and R (-√6, -√6) is an equilateral triangle. (3)

6.   The line joining the points (2, -1) and (5, -6) is bisected at p. If p lies on line 2x + 4y + k = 0, find the value of k. (3)

7.   If p (x, y) is any point on the line joining the points A (a, 0) and B (0, b), then show that x/a + y/b = 1. (3)

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

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. (4)

10.   Find the distance between the points (3, -5) and (2, 6). (2)