Question

AJKL has vertices at 3(-4,-2), K(1,-1), and (-2,-4). Determine if AJKL is a right triangle.

Answer 1

To determine if AJKL is a right triangle, we can calculate the distances between its vertices and check if they satisfy the Pythagorean theorem.

Step-by-step explanation:

To determine if AJKL is a right triangle, we can calculate the distances between its vertices and check if they satisfy the Pythagorean theorem. Let's denote the distances as d1, d2, and d3.

d1 = sqrt((-4-1)^2 + (-2+1)^2) = sqrt(25) = 5

d2 = sqrt((-4+2)^2 + (-2+4)^2) = sqrt(8) ≈ 2.83

d3 = sqrt((-2+4)^2 + (-4-2)^2) = sqrt(40) ≈ 6.32

Since the sum of the squares of the lengths of the two shorter sides (d1 and d2) is approximately equal to the square of the length of the longest side (d3), AJKL is a right triangle.