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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=12andy+12=1
x=2andy=1
Hence, the fourth vertex of the parallelogram is (-2, 1)

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