SOLUTION: Consider the three points A=(2,12) B=(4,16) C=(6,15). Determine whether the triangle ABC is a right triangle. Explain your reasoning.

Algebra ->  Test -> SOLUTION: Consider the three points A=(2,12) B=(4,16) C=(6,15). Determine whether the triangle ABC is a right triangle. Explain your reasoning.      Log On


   

Question 537534: Consider the three points A=(2,12) B=(4,16) C=(6,15). Determine whether the triangle ABC is a right triangle. Explain your reasoning.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
three points A=(2,12) B=(4,16) C=(6,15).
l( AB) = Distance between two points
x1 y1 x2 y2
d= sqrt%28%28y2-y1%29%5E2%2B%28x2-x1%29%5E2%29
2 12 4 16
d= sqrt%28%2816-12%09%29%5E2%09%2B%09%284-2%29%5E2%09%29
d= sqrt%28%284%29%5E2%09%2B%282%29%5E2%09%29
d= sqrt%28%2820%29+%09%29
d= 4.472
l(BC)=Distance between two points
x1 y1 x2 y2
d= sqrt%28%28y2-y1%29%5E2%2B%28x2-x1%29%5E2%29
4 16 6 15
d= sqrt%28%28%09%0915%09-%0916%09%29%5E2%09%2B%09%28%096%09-%094%09%29%5E2%09%29
d= sqrt%28%28%09%09-1%09%29%5E2%09%2B%09%28%092%09%29%5E2%09%29
d= sqrt%28%28%09%095%09%29++%09%29
d= 2.236
l(CA)=x1 y1 x2 y2
d= sqrt%28%28y2-y1%29%5E2%2B%28x2-x1%29%5E2%29
6 15 2 12
d= sqrt%28%28%09%0912%09-%0915%09%29%5E2%09%2B%09%28%092%09-%096%09%29%5E2%09%29
d= sqrt%28%28%09%09-3%09%29%5E2%09%2B%09%28%09-4%09%29%5E2%09%29
d= sqrt%28%28%09%0925%09%29++%09%29
d= 5

CHECK for pythagoras theorem
(4.472)^2+(2.24)^2= 5^2
So it is right triangle
m.ananth@hotmail.ca