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Explanation:
The quadrilateral will be a parallelogram if the diagonals bisect each other. That is, their midpoints are the same point. We don't actually need to calculate the midpoint. Rather, we can calculate the point that has double the coordinate values.
If (A+C) = (B+D), the quadrilateral is a parallelogram.
A +C = B +D
(-2, 8) +(5, 1) = (2, 7) +(1, 2)
(-2+5, 8+1) = (2+1, 7+2)
(3, 9) = (3, 9) . . . . . the figure is a parallelogram
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Of course, the midpoint of the diagonals is (3/2, 9/2).
