Scott said that \( \triangle A B C \) denoted by the coordinates \( A(2,3) B(8,3) C(5,8) \) is equilateral. Yes, he is correct, the side lengths are 6 . No, it is an isosceles triangle with legs lengths of 6 No, it is an isosceles triangle with legs lengths of \( \sqrt{34} \). Yes, he is correct, the side lengins are \( \sqrt{34} \).

To determine the type of triangle \( \triangle ABC \), we need to calculate the lengths of its sides using the distance formula: \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \). For sides \( AB, AC, \) and \( BC \), the lengths are \( AB = 6 \), \( AC = \sqrt{34} \), and \( BC = \sqrt{34} \). This means \( \triangle ABC \) is indeed isosceles, not equilateral. In triangles, understanding the properties can prevent common mistakes. A common pitfall is assuming all sides are equal just because it looks that way visually. Always calculate the lengths to confirm! In this case, we can see clearly that while two sides are equal, all three sides are not, which distinguishes an isosceles triangle from an equilateral one.