Question

prove that (-1,4) , (-3,-6) and (3,-2) are the vertices of an isosceles right triangle

Answer 1

Let's assume the sides of ∆ as AB, BC and CA.

AB = √[(- 1 + 3)² + (4 + 6)²] = √104

BC = √[(3 + 3)² + (- 2 + 6)²] = √52

CA = √[(3 + 1)² + (- 2 - 4)²] = √52

Hence we get BC = CA = √52.

Since we know that triangle having two sides equal is called isosceles triangle.

Hence Proved