Select the correct answer The points D(-2,2),E(2,5) and F(5,1) form Delta DEF in the coordinate plane What condition verifies that the triangle is a right triangle? A The product of the slopes of two of the sides is 1 B. The prouct of the slopes of two of the sides is -1 C. Three of the of the triangle are equal D. Two of the sides of the triangle are equal.

To determine if the triangle DEF is a right triangle, we need to check if the product of the slopes of two of its sides is -1. This is because the product of the slopes of two perpendicular lines is -1.<br /><br />Let's calculate the slopes of the sides of the triangle:<br /><br />Slope of DE = (5 - 2) / (2 - (-2)) = 3/4<br />Slope of EF = (1 - 5) / (5 - 2) = -4/3<br />Slope of DF = (1 - 2) / (5 - (-2)) = -1/7<br /><br />Now, let's check the product of the slopes of two sides:<br /><br />Product of slopes of DE and EF = (3/4) * (-4/3) = -1<br /><br />Since the product of the slopes of DE and EF is -1, it confirms that the triangle DEF is a right triangle.<br /><br />Therefore, the correct answer is B. The product of the slopes of two of the sides is -1.