SOLUTION: Prove that the triangle with vertices(13,-1),(-9,3),(-3,-9) is a right triangle.

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Question 135147: Prove that the triangle with vertices(13,-1),(-9,3),(-3,-9) is a right triangle.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let's name the points
A (13,-1)
B (-9,3)
C (-3,-9)
For a right triangle the sums of the squares of the two legs equal the square of the hypotenuse, the longest leg.
Calculate each leg length first using the distance formula between two points.
D%5E2=%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2
AB, the distance from point A to point B.
%28AB%29%5E2=%2813-%28-9%29%29%5E2%2B%28-1-3%29%5E2
%28AB%29%5E2=%2822%29%5E2%2B%284%29%5E2
%28AB%29%5E2=484%2B16
%28AB%29%5E2=500
AC, the distance from point A to point C.
%28AC%29%5E2=%2813-%28-3%29%29%5E2%2B%28-1-%28-9%29%29%5E2
%28AC%29%5E2=%2816%29%5E2%2B%288%29%5E2
%28AC%29%5E2=256%2B64
%28AC%29%5E2=320
BC, the distance from point B to point C.
%28BC%29%5E2=%28-9-%28-3%29%29%5E2%2B%283-%28-9%29%29%5E2
%28BC%29%5E2=%28-6%29%5E2%2B%2812%29%5E2
%28BC%29%5E2=36%2B144
%28BC%29%5E2=180
Since AB is the largest, it is the hypotenuse.
If it is a right triangle then,
%28AB%29%5E2=%28AC%29%5E2%2B%28BC%29%5E2
500=320%2B180
500=500
True statement.
Those point, therefore, define a right triangle.