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Question
Prove that the points (0 , 0) , (3 , 2) , (7 , 7) and (4 , 5) are the vertices of a parallelogram.
Solution
AB = `sqrt ((3 - 0)^2 + (2 - 0)^2) = sqrt (9 + 4) = sqrt 13` units
BC = `sqrt ((3 - 7)^2 + (2 - 7)^2) = sqrt (16 + 25) = sqrt 41` units
CD = `sqrt ((7 - 4)^2 + (7 - 5)^2) = sqrt (9 + 4) = sqrt 13` units
DA = `sqrt ((4 - 0)^2 + (5 - 0)^2) = sqrt (16 + 25) = sqrt 41` units
∵ AB = CD and BC = DA
∴ ABCD is a parallelogram.
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