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

To determine if triangle \( ABC \) is equilateral, we first calculate the lengths of its sides using the distance formula. The length of side \( AB \) is \( 8 - 2 = 6 \), side \( AC \) is \( \sqrt{(5-2)^2 + (8-3)^2} = \sqrt{9 + 25} = \sqrt{34} \), and side \( BC \) is \( \sqrt{(8-5)^2 + (3-8)^2} = \sqrt{9 + 25} = \sqrt{34} \). The unequal lengths indicate it's an isosceles triangle (two sides equal), hence Scott is incorrect. For a triangle to be equilateral, all three sides must be of equal length. Here, we found two sides measuring \( \sqrt{34} \) and one side measuring \( 6 \). Since the lengths \( 6 \) and \( \sqrt{34} \) are not equal, Scott's claim of \( \triangle ABC \) being equilateral does not hold true! So it's definitely an isosceles triangle, not equilateral.