I need help putting this into an equation

Question

How do I determine if this is a right triangle or not? How do I put it into an equation?

There are 3 points ABC in the xy-plane have coordinates A(4, 3) B (-6, 2) C (-5, 7)

Thanks so much for your help!

Answer 1

distance squared from A to B = 1 + 100 = 101

3-2 squared plus 4--6 squared

distance squared from B to C = 1 + 25 = 26

-6 --5 squared plus 7-2 squared

distance squared from A to C = 81 + 16 = 97

4--5 squared plus 7-3 squared

If it's a right triangle 101 = 97 + 26. the longest side would be the hypotenuse which squared equals the sum of squares of the other two sides. That's not true, so it's not a right triangle. 101 does not equal 97 + 26.