Question

The points D(-2,2), E(2,5) , and F(5,1) form △ DEF in the coordinate plane. What condition verifies that the triangle is a right triangle?

A. Three of the sides of the triangle are equal.
B. The product of the slopes of two of the sides is 1.
C. Two of the sides of the triangle are equal.
D. The product of the slopes of two of the sides is -1.

Answer 1

The condition that verifies that the triangle DEF is a right triangle is that the product of the slopes of two of its sides is -1.

Step-by-step explanation:

In order to verify that the triangle △DEF is a right triangle, we can check if the product of the slopes of two of its sides is -1.

We will calculate the slopes of the sides DE and EF using the formula: slope = (y2 - y1) / (x2 - x1).

The slope of DE is (5 - 2) / (2 - (-2)) = 3/4, and the slope of EF is (1 - 5) / (5 - 2) = -4/3.

The product of these slopes is (3/4) * (-4/3) = -1. Since the product is -1, the condition is verified and △DEF is a right triangle. The answer is option D.