Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle

Let us assume that points (5, - 2), (6, 4), and (7, - 2) are representing the vertices A, B, and C of the given triangle respectively

AB = [(5- 6)² + (-2- 4)²]^1/2

BC = [(6- 7)² + (4+ 2)²]^1/2

CA = [(5- 7)² + (-2+ 2)²]^1/2

= 2

Therefore, AB = BC

As two sides are equal in length, therefore, ABCis an isosceles triangle