How to find the fourth coordinate of a parallelogram?
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Consider A(3, 4), B (3, 8) and C(9, 8). Let D (x, y) be the fourth vertex of the parallelogram ABCD. Midpoint of AC = [( 3+ 9 ) / 2 , (4 + 8) / 2] = (6,6) Midpoint of BD = [( x + 3 ) / 2 , (y + 8) / 2]
Since, the diagonals of parallelogram bisect each other at O.
∴ Mid point of BD = Mid point of AC [( x + 3 ) / 2 , (y + 8) / 2] = (6,6) (x + 3) / 2 = 6 and (y + 8) / 2 = 6 x + 3 = 12 and y + 8 = 12 x = 9 and y = 4
∴ (9, 4) is the fourth vertex.
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