The vertices of a triangle are labeled clockwise a(–5, 3), b(6, 1), and c(–2, –3). how could you show that the figure is a right triangle?

1. Check the picture attached.

2. The best thing to do first in this problem is to draw an accurate figure.

3. By the figure it is clear that the right angle is going to be at C.

4. We are going to prove that . If this holds, then the sides are "pythagorean triples", that is ABC is a right triangle.

5. 






Remark: The lengths of AB, BC and AC can be also found directly by applying the formula of the distance between 2 points whose coordinates are given. 

Subtract 2 from all the first numbers and add 3 to all the second ones for new coordinates