Quadrilateral ABCD has vertices AC-3.6), B(6,0), C(9. -9), and D(0, -3). Prove that ABCD is a) a parallelogram
1 answer:
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Explanation:
The quadrilateral will be a parallelogram if the diagonals bisect each other. That will be the case if the sums of their end-point coordinates are the same.
A + C = (-3, 6) +(9, -9) = (6, -3)
B + D = (6, 0) +(0, -3) = (6, -3)
Both diagonals have their midpoint at (3, -1.5), so the diagonals are mutual bisectors. The figure ABCD must be a parallelogram.
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The midpoint of AC is (A+C)/2 = (6, -3)/2 = (3, -1.5).
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