C1 question help

Translating from welsh so bear with me:

"The Coordinates of A, B, and C are (6, -3), (-10,9) and (12,5), respectively. Find out the lengths of the lines AB, BC, CA. Prove it is a right angle triangle"

I've found out the lengths (AB: 20, BC: 10√5, CA: 10), but i don't know how to prove it's a right angle triangle.

Work out the gradient of the three lines. If there is a right angle, there must be two lines that are perpendicular to each other meaning:

(gradient of line 1) * (gradient of line 2) = -1

So if there was a line that had gradient 3/4 and another that had gradient -4/3, then those two lines are perpendicular so there would be a right angle.

What you did there was just the first step.


Btw, I'm also doing C1, so I'm not exactly sure I'm getting this correct.

This is also a nice method that I will keep in mind. Thanks