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प्रश्न
Prove that the points (0 , 2) , (1 , 1) , (4 , 4) and (3 , 5) are the vertices of a rectangle.
उत्तर
AB = `sqrt ((0 - 1)^2 + (2 - 1)^2) = sqrt 2` units
BC = `sqrt ((1 - 4)^2 + (1 - 4)^2) = 3 sqrt 2` units
CD = `sqrt ((4 - 3)^2 + (4 - 5)^2) = sqrt 2` units
DA = `sqrt ((3 - 0)^2 + (5 - 2)^2) = 3 sqrt 2` units
AC = `sqrt ((4 - 0)^2 + (4 - 2)^2) = sqrt 20 = 2 sqrt 5` units
BC = `sqrt ((3 - 1)^2 + (5 - 1)^2) = sqrt 20 = 2 sqrt 5` units
∵ AB = CD and BC = DA
Also , AC = BD
∴ ABCD is a rectangle.
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