Question

Prove that the points (1 ,1),(-4 , 4) and (4 , 6) are the certices of an isosceles triangle.

Answer 1

PQ = `sqrt ((1 + 4)^2 + (1 - 4)^2) = sqrt (25 + 9) = sqrt 34` units

QR = `sqrt ((-4-4)^2 + (4 - 6)^2) = sqrt (64 + 4) sqrt 68` units

PR = `sqrt ((4 - 1)^2 + (6 - 1)^2) = sqrt (9 + 25) = sqrt 34` units

∵  PQ = QR

∴ P,Q and R are the vertices of an isosceles triangle.