△GHI has vertices at G(–9,5), H(–3,9), and I(–4,4).Is △GHI an isosceles triangle? Justify your answer.

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

1. Calculate the length of GH: √[(-3 - -9)² + (9 - 5)²] = √[(6)² + (4)²] = √[36 + 16] = √52

2. Calculate the length of HI: √[(-4 - -3)² + (4 - 9)²] = √[(1)² + (-5)²] = √[1 + 25] = √26

3. Calculate the length of GI: √[(-4 - -9)² + (4 - 5)²] = √[(5)² + (-1)²] = √[25 + 1] = √26

From the calculations, we can see that GH ≠ HI but HI = GI. Therefore, △GHI is an isosceles triangle because two of its sides (HI and GI) have the same length.