Example-17.

If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram, taken inorder, find the value of p.

Solution :

We know that diagonals of parallelogram bisect each other. So, the coordinates of the midpoint of AC = Coordinates of the midpoint of BD.



EXERCISE - 7.2

1. Find the coordinates of the point which divides the line segment joining the points (-1, 7) and (4, -3) in the ratio 2 : 3.

2. Find the coordinates of the points of trisection of the line segment joining (4, -1) and (-2, -3).

3. Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6).

4. If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.

5. Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, -3) and B is (1, 4).

6. If A and B are (-2, -2) and (2, -4) respectively, find the coordinates of P on AB such that AP = 3 7 AB.

7. Find the coordinates of points which divide the line segment joining A(-4, 0) and B(0, 6) SCERT into four equal parts.



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