Chapter 17: Co-ordinate Geometry

Exercise - 32

1. A(3, 2) and B(-2, 1) are two vertices of a triangle ABC, whose centroid has coordinates (5/3, -1/3). Find the coordinates of the third vertex C of the triangle.
2. Show that the points A(2, -2), B(14, 10), C(11, 13) and D(-1, 1) are the vertices of a rectangle.
3. Determine the ratio in which the points (6, a) divides the join of A(-3, -1) and B(-8, 9). Also find the value of a.
4. Find the point on the x-axis which is equidistant from the points (-2, 5) and (2, -3).
5. The co-ordinates of the mid-point of the line joining the points (3p, 4) and (-2, 2q) are (5, p). Find the values of p and q.
6. Two vertices of a triangle are (1, 2) and (3, 5). If the centroid of the triangle is at the origin, find the coordinates of the third vertex.
7. If ‘a’ is the length of one of the sides of an equilateral triangle ABC, base BC lies on x-axis and vertex B is at the origin, find the coordinates of the vertices of the triangle ABC.
8. The coordinates of the mid-point of the line joining the points (2p+1, 4) and (5, q – 1) are (2p, q). Find the value of p and q.
9. The coordinates of two vertices A and B of a triangle ABC are (1, 4) and (5, 3) respectively. If the coordinates of the centroid of triangle ABC are (3, 3), find the coordinates of the third vertex C.
10. Find the value of k for which the points with coordinates (3, 2), (4, K) and (5, 3) are collinear.
11. Find the value of k for which the points with coordinates (2, 5), (k, 11/2) and (4, 6) are collinear.

Answers

1. (4, -4)	3. 3 : 2, 5	4. (-2, 0)
5. 4, 2	6. (-4, -7)	7.
8. 3, 3	9. (3, 2)	10. 5/2