Triangle abc has vertices at a(–2, 3), b(–3, –6), and c(2, –1). is triangle abc a right triangle? if so, which angle is the right angle?

We'll use rise over run to find the slopes of two of the sides of the triangle:



Because C is the rightmost point, we'll have it represent (x1,y1), and have A and B represent (x2,y2):

A to C
(-2,3) to (2,-1)



The slope of the line from A to C is -1.

B to C
(-3,-6) to (2,-1)



The slope of the line from B to C is 1.

These lines intersect at (2,-1), and they have negative reciprocal slopes of each other, which creates a perpendicular angle. This means that triangle ABC is a right triangle, and angle ACB is the right angle.