Question

Prove that the points (0 , 2) , (1 , 1) , (4 , 4) and (3 , 5) are the vertices of a rectangle.

Answer 1

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.