What are we really trying to do? Prove that RUN is a right triangle.

I already graphed it and it is a right triangle but how do I prove it...

show that it's legs satisfy the pythagorean formula

\(|RU|^2 = (6-1)^2+(-1-(-1))^2 = 25\\ |RN|^2 = (1-1)^2+(-7-(-1))^2= 64\\ |NU|^2 = (6-1)^2 + (-1-(-7))^2 = 5^2 + 8^2 = 25+64\\ \text{clearly }|RU|^2 + |RN|^2 = |NU|^2 \text{ and thus this must be a right triangle}\)

Thank you ouo