Question

Three vertices of a parallelogram are shown in the figure below.

Give the coordinates of the fourth vertex.
(-3,-2)
(2,-8)
(6,-4)

Answer 1

(-7, -6)

Explanation:

You want the coordinates of the fourth vertex of the parallelogram with adjacent vertices (-3, -2), (6, -4) and (2, -8).

Diagonals

The diagonals of a parallelogram bisect each other, so their midpoints are the same point. If the given vertices are A, B, C, then D must satisfy ...

(A +C)/2 = (B +D)/2

D = A +C -B

D = (-3, -2) +(2, -8) -(6, -4) = (-3+2-6, -2-8+4)

D = (-7, -6)

The fourth vertex has coordinates (-7, -6).

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