Question

Prove that the points (0 , -4) , (6 , 2) , (3 , 5) and (-3 , -1) are the vertices of a rectangle.

Answer 1

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.