Question
In parallelogram ABCD, coordinates are A(1, 2), B(5, 4)
and C(7, 6). Find the coordinates of D and the area of the parallelogram.Solution
In a parallelogram, A + C = B + D (vector form). Let D(x, y): A(1,2) + C(7,6) = B(5,4) + D(x,y) (1+7, 2+6) = (5 + x, 4 + y) (8, 8) = (5 + x, 4 + y) So x = 3, y = 4 D(3, 4) Area of parallelogram = magnitude of cross product of adjacent sides. Vectors AB = (5−1, 4−2) = (4,2) AD = (3−1, 4−2) = (2,2) Area = |ABₓ·ADᵧ − ABᵧ·ADₓ| = |4×2 − 2×2| = |8 − 4| = 4 square units.
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