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Question

The three vertices of a parallelogram taken in order are (–1, 0), (3, 1) and (2, 2) respectively. Find the coordinates of the fourth vertex


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Solution

Let A (-1, 0), B (3, 1), C (2, 2) and D(x, y) be the vertices of a parallelogram ABCD taken in order.

Since, the diagonals of a parallelogram bisect each other.

Coordinates of the mid-point of AC = Coordinates of the mid-point of BD

(1+22,0+22) = (3+x2,1+y2)

(12,1) = (3+x2,y+12)

3+x2=12 and y+12=1

x = -2 and y = 1

Hence, the fourth vertex of the parallelogram is (-2, 1).


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