Question

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

Answer 1

AB = `sqrt ((5-1)^2 + (3 -2)^2) = sqrt (16 + 1) = sqrt 17` units

BC = `sqrt ((1 - 2)^2 + (2 + 2)^2) = sqrt (1 + 16) = sqrt 17` units

CD = `sqrt ((6 - 2)^2 + (-1 + 2)^2) = sqrt (16 + 1) = sqrt 17` units

DA = `sqrt ((6 - 5)^2 + (- 1 - 3)^2) = sqrt (1 + 16) = sqrt 17` units

AC = `sqrt ((5 - 2)^2 + (3 + 2)^2) = sqrt (9 +25) = sqrt 34` units

BD = `sqrt ((6-1)^2 + (-1 -2)^2) = sqrt (25 + 9) = sqrt 34` units

∵ AB = BC = CD = DA and AC = BD

∴ ABCD is a square.