△TUV has vertices at T(–8,5), U(7,1), and V(1,–7).Is △TUV an isosceles triangle? Justify your answer.

To determine if △TUV is an isosceles triangle, we need to check if any two sides of the triangle are of equal length. We can do this by using the distance formula, which is √[(x₂ - x₁)² + (y₂ - y₁)²].

1. Calculate the distance between T and U: √[(7 - (-8))² + (1 - 5)²] = √[225] = 15

2. Calculate the distance between U and V: √[(1 - 7)² + (-7 - 1)²] = √[100] = 10

3. Calculate the distance between T and V: √[(-8 - 1)² + (5 - (-7))²] = √[225] = 15

As we can see, the distance between T and U is equal to the distance between T and V (both are 15 units). Therefore, △TUV is an isosceles triangle.