SOLUTION: Is ΔABC with vertices A(–2, 3), B(2, 0), and C(–1, –4) a right triangle? Please answer with: ΔABC is a right triangle because or ΔABC is not a right tria

Algebra ->  Triangles -> SOLUTION: Is ΔABC with vertices A(–2, 3), B(2, 0), and C(–1, –4) a right triangle? Please answer with: ΔABC is a right triangle because or ΔABC is not a right tria      Log On


   

Question 810650: Is ΔABC with vertices A(–2, 3), B(2, 0), and C(–1, –4) a right triangle?
Please answer with:
ΔABC is a right triangle because or
ΔABC is not a right triangle.
Thank You.


Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
A(–2, 3), B(2, 0), and C(–1, –4)
find the distance between AB, BC, & CA
AB
Distance between two points
x1 y1 x2 y2

-2 3 2 0
d= sqrt%28%28y2-y1%29%5E2%2B%28x2-x1%29%5E2%29
d= sqrt%28%28%09%090%09-%093%09%29%5E2%09%2B%09%28%092%09-%09-2%09%29%5E2%09%29
d= sqrt%28%28%09%09-3%09%29%5E2%09%2B%09%28%094%09%29%5E2%09%29
d= sqrt%28%28%09%0925%09%29++%09%29
d= 5.00
distance BC
Distance between two points
x1 y1 x2 y2

2 0 -1 -4
d= sqrt%28%28y2-y1%29%5E2%2B%28x2-x1%29%5E2%29
d= sqrt%28%28%09%09-4%09-%090%09%29%5E2%09%2B%09%28%09-1%09-%092%09%29%5E2%09%29
d= sqrt%28%28%09%09-4%09%29%5E2%09%2B%09%28%09-3%09%29%5E2%09%29
d= sqrt%28%28%09%0925%09%29++%09%29
d= 5.00
Distance CA
x1 y1 x2 y2

-2 3 -1 -4
d= sqrt%28%28y2-y1%29%5E2%2B%28x2-x1%29%5E2%29
d= sqrt%28%28%09%09-4%09-%093%09%29%5E2%09%2B%09%28%09-1%09-%09-2%09%29%5E2%09%29
d= sqrt%28%28%09%09-7%09%29%5E2%09%2B%09%28%091%09%29%5E2%09%29
d= sqrt%28%28%09%0950%09%29++%09%29
d= 7.07
AB=5,BC=5 & AC=7.07
ab^2+BC^2= is not equal to AC^2
therefore it is not a right triangle