Question

Prove that the points (1 , 1) , (-1 , -1) and (`- sqrt 3 , sqrt 3`) are the vertices of an equilateral triangle.

Answer 1

PQ = `sqrt ((1 + sqrt 3)^2 + (1 - sqrt 3)^2) = sqrt (4 + 4) sqrt 8` units

QR = `sqrt ((-sqrt 3 + 1)^2 + (sqrt 3 + 1)^2) = sqrt (4 + 4) = sqrt 8` units

PR = `sqrt ((- 1 + 1)^2 + (-1 + 1)^2) = sqrt (4 + 4) = sqrt 8` units

∵ PQ = QR = PR

∴ PQR is an equilateral triangle.