James said that \( \Delta \mathrm{JKL} \) denoted by the coordinates \( \mathrm{J}(3,5) \mathrm{K}(3,8) \mathrm{L}-4,8) \) is an isosceles triangle. Is he correc He is incorrect, because there is not enough information to determine what time of triangle it is. Yes, he is correct. He is incorrect because it is a scalene right triangle. He is incorrect. It is an equilateral triangle.

Let's first list the coordinates of the vertices of ΔJKL: • J = (3, 5) • K = (3, 8) • L = (–4, 8) Step 1: Calculate the side lengths. • Side JK:   Distance between J(3,5) and K(3,8)   = √[(3 – 3)² + (8 – 5)²] = √[0 + 3²] = 3. • Side KL:   Distance between K(3,8) and L(–4,8)   = √[(–4 – 3)² + (8 – 8)²] = √[(-7)² + 0] = 7. • Side JL:   Distance between J(3,5) and L(–4,8)   = √[(–4 – 3)² + (8 – 5)²] = √[(-7)² + 3²] = √(49 + 9) = √58. Step 2: Examine the triangle type. • For an isosceles triangle, at least two sides must be equal in length. Here, the sides are 3, 7, and √58 (approximately 7.62), so no two sides are equal. • Notice that segment JK is vertical and segment KL is horizontal. This means they are perpendicular. Thus, the angle at vertex K is 90° and ΔJKL is a right triangle. • Since all three sides have different lengths, the triangle is scalene. Answer: James is incorrect because ΔJKL is a scalene right triangle.