Coordinate Geometry-Sample Questions

1.   Find the area of the triangle ABC with A (1, - 4) and mid-points of sides through A being (2, - 1) and (0, -1). (CBSE 2015)

2.   Find the ratio in which the point P (3/4, 5/12) divides the line segment joining the points A (1/2, 3/2) and B (2, -5). (CBSE 2015)

3.   If A(-4, 8), B(-3, -4), C(0, -5) and D(5, 6) are the vertices of a quadrilateral ABCD, find its area. (CBSE 2015)

4.   Find the coordinates of the point P dividing the line segment joining the points A (1, 3) and B (4, 6) in the ratio 2:1. (CBSE 2012)

5.   If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (-2, 5), then what are the coordinates of the other end of the diameter? (CBSE 2012)

6.   If a point A (0, 2) is equidistant from the points B (3, p) and C (p, 5), then find the value of p. (CBSE 2012)

7.   Prove that the points (7, 10), (-2,5) and (3,-4) are the vertices of an isosceles right triangle. (CBSE 2013)

8.   Find the ratio in which the y-axis divides the line segment joining the points (-4,-6) and (10, 12). Also find the coordinates of the point of division. (CBSE 2013)

9.   If the points A(x, 2), B (-3,-4) and C (7, -5) are collinear, then what is the value of x? (CBSE 2014)

10.   If the point A (0, 2) is equidistant from the points B(3, p) and C(p, 5), find P. Also find the length of AB. (CBSE 2014)

11.   The mid-point of segment AB is the point P (0, 4). If the Coordinates of B are (-2, 3) then find the coordinates of A. (CBSE 2011)

12.   If two vertices of an equilateral triangle are (3, 0) and (6, 0), find the third vertex. (CBSE 2011)

13.   Find the point of y-axis which is equidistant from the points (-5, -2) and (3, 2). (CBSE 2011)

14.   If two vertices of an equilateral triangle are (3, 0) and (6, 0), find the third vertex. (CBSE 2011)