SOLUTION: Are these 3 points the vertices of a right triangle (-9,5), (-7,9), (-5,8). I answered no but not sure if I am doing it right. Also are these 3 points Collinear (-7,0), (-2,4),

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Are these 3 points the vertices of a right triangle (-9,5), (-7,9), (-5,8). I answered no but not sure if I am doing it right. Also are these 3 points Collinear (-7,0), (-2,4),       Log On


   

Question 1031395: Are these 3 points the vertices of a right triangle (-9,5), (-7,9), (-5,8).
I answered no but not sure if I am doing it right.
Also are these 3 points Collinear (-7,0), (-2,4), (-11,-5)
I answered no on that one also.
Can you explain how you got your answer so I know how to do it please.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let the points be P(-9,5), Q(-7,9), R(-5,8).
==> Line PQ has slope m%5BPQ%5D+=+%289-5%29%2F%28-7%2B9%29+=+4%2F2+=+2
Line QR has slope m%5BQR%5D+=+%288-9%29%2F%28-5%2B7%29+=+-1%2F2, and line PR has slope m%5BPR%5D+=+3%2F4.
Sonce m%5BPQ%5D%2Am%5BQR%5D+=+-1, it follows that line PQ is perpendicular to line QR, and the vertices form a right triangle.
As for the points (-7,0), (-2,4), (-11,-5), they are NOT collinear, because the area of the triangle formed by these points is not equal to 0. (If so, they would be collinear.)
Area = .