Question

Prove that the points (6 , -1) , (5 , 8) and (1 , 3) are the vertices of an isosceles triangle.

Answer 1

AB = `sqrt ((6 - 5)^2 + (-1-8)^2) = sqrt (1 + 81) = sqrt 82` units

BC = `sqrt ((5-1)^2 + (8 - 3)^2) = sqrt (16+25) = sqrt 41` units

AC = `sqrt ((1-6)^2 + (3 - 1)^2) = sqrt (25 + 16) = sqrt 41` units

∵ BC = AC

∴ A , B and C are the vertices of an isosceles triangle.