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Question
Show that the given points form a parallelogram:
A(2.5, 3.5), B(10, – 4), C(2.5, – 2.5) and D(– 5, 5)
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Solution
Let A(2.5, 3.5), B(10, – 4), C(2.5, – 2.5) and D(– 5, 5) are the vertices of a parallelogram.
Slope of a line = `(y_2 - y_1)/(x_2 - x_1)`
Slope of AB = `(-4 - 3.5)/(10 - 2.5) = (-7.5)/(7.5)` = – 1
Slope of CD = `(5 + 2.5)/(-5 - 2.5) = (7.5)/(-7.5)` = – 1
Slope of AB = Slope of CD = – 1
∴ AB is Parallel to CD ...(1)
Slope of BC = `(-4 + 2.5)/(10 - 2.5) = (-1.5)/(7.5) = (-15)/75 = -1/5`
Slope of AD = `(5 - 3.5)/(-5 - 2.5) = 1.5/-7.5 = 15/(-75) = -1/5`
Slope of BC = Slope of AD
∴ BC is parallel to AD
From (1) and (2) we get ABCD is a parallelogram.
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