Question

Prove that the points (7 , 10) , (-2 , 5) and (3 , -4) are vertices of an isosceles right angled triangle.

Answer 1

AB = `sqrt ((7 + 2)^2 + (10 - 5)^2) = sqrt (81 + 25) = sqrt 106` units

BC = `sqrt ((-2-3)^2 + (5 + 4)^2) = sqrt (25 + 81) = sqrt 106` units

AC = `sqrt ((7 - 3)^2 + (10 + 4)^2) = sqrt (16 + 196) = sqrt 212` units

∵ AB = BC

∴ ABC is an isosceleles triangle

AB² + BC² = 100 + 106 = 212

AC² = 212

∵ AB² + BC² = AC²

∴ ABC is also a right angled triangle.