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Question
Prove that the points (0 , -4) , (6 , 2) , (3 , 5) and (-3 , -1) are the vertices of a rectangle.
Solution
AB = `sqrt ((6 - 0)^2 + (2 + 4)^2) = 6 sqrt 2` units
BC = `sqrt ((6 - 3)^2 + (2 - 5)^2) = 3 sqrt 2` units
CD = `sqrt ((3 + 3)^2 + (5 + 1)^2) = 6 sqrt 2` units
DA = `sqrt ((- 3 - 0)^2 + (-1 + 4)^2) = 3 sqrt 2` units
AC = `sqrt ((3 - 0)^2 + (5 + 4)^2) = 3 sqrt 10` units
BD = `sqrt ((6 + 3)^2 + (2 + 1)^2) = 3 sqrt 10` units
∵ AB = CD and BC = DA ,
Also AC = BD
∴ ABCD is a rectangle.
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