SOLUTION: I have a question. what do you do if you need to prove a triangle is a right triangle, but you only have variable coordinates for that triangle. Here's what I have so far: Triangle

Algebra ->  Pythagorean-theorem -> SOLUTION: I have a question. what do you do if you need to prove a triangle is a right triangle, but you only have variable coordinates for that triangle. Here's what I have so far: Triangle      Log On


   

Question 562913: I have a question. what do you do if you need to prove a triangle is a right triangle, but you only have variable coordinates for that triangle. Here's what I have so far: Triangle ABC: A(x,0); B(x,y); C(2x,0)
Finding AB: sqrt%28%28x-x%29%5E2%2B%28y-0%29%5E2%29
sqrt%282y%29
Finding BC: sqrt%28%282x-x%29%5E2%2B%280-y%29%5E2%29
sqrt%28x%5E2=y%5E2%29
Finding AC: sqrt%28%282x-x%29%5E2%2B%280-0%29%5E2%29
sqrt%28x%5E2%29
Final Steps: a^2+b^2=c^2
sqrt%28%282y%29%29%5E2%2B+sqrt%28%28x%5E2%29%29%5E2=+sqrt%28%28x%5E2%2By%5E2%29%29%5E2
sqrt%284y%5E2%29%2B+sqrt%282x%5E4%29=+sqrt%28x%5E4%2By%5E4%29
I'm confused on what to do next. I know that if a^2+b^2=c^2 then it is a right triangle. But, I can't solve it any furthur. I also can't use sin, cos, or tan. Thannk you in advance.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Triangle ABC: A(x,0); B(x,y); C(2x,0)
Finding AB: sqrt%28%28x-x%29%5E2%2B%28y-0%29%5E2%29
sqrt%28y%5E2%29
=y
Finding BC: sqrt%28%282x-x%29%5E2%2B%280-y%29%5E2%29
sqrt%28x%5E2%2By%5E2%29
Finding AC: sqrt%28%282x-x%29%5E2%2B%280-0%29%5E2%29
sqrt%28x%5E2%29
=x
Final Steps: a^2+b^2=c^2
%28sqrt%28x%5E2%29%29%5E2%2B%28sqrt%28y%5E2%29%29%5E2=+%28sqrt%28x%5E2%2By%5E2%29%29%5E2
m.ananth@hotmail.ca