Question

How do you show that the triangle with verticies D ( -2,5), E (- 4,1), F (2,3) is a right angle triangle?

Answer 1

Prove right triangle

Explanation:

We prove that line DE is perpendicular to DF by showing that the product oftheir slopes is (-1).
Slope of line ED:
(yD - yE)/(xD - xE) = (5 - 1 )/(-2 + 4) = 4/2 = 2
Slope of EF:
(yF - yD)/(xF - xD) = (3 - 5)/(2 + 2) = -2/4 = -1/2.
The product of the 2 slopes is (-1), therefor, the triangle DEF is a right triangle.