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Question

Three vertices of a parallelogram, taken in order, are (−1, −6), (2, −5) and (7, 2). Write the coordinates of its fourth vertex.

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Solution

Let A-1,-6, B2,-5 and C7, 2 be the vertices of the parallelogram ABCD.
Let the coordinates of D be (x, y).

Since, diagonals of a parallelogram bisect each other,

-1+72=2+x2 and -6+22=-5+y2x=4 and y=1

Hence, the coordinates of the fourth vertex D are (4, 1).

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