SOLUTION: Determine whether it is possible to have a triangle with the given vertices. Write yes or no, and explain your answer. (CH.5-5) A(-2,-2) B(-1,1) C(1,4)

Algebra ->  Formulas -> SOLUTION: Determine whether it is possible to have a triangle with the given vertices. Write yes or no, and explain your answer. (CH.5-5) A(-2,-2) B(-1,1) C(1,4)      Log On


   

Question 401043: Determine whether it is possible to have a triangle with the given vertices. Write yes or no, and explain your answer. (CH.5-5)
A(-2,-2) B(-1,1) C(1,4)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Any three non-collinear (not on the same line) points can make a triangle. So all we have to do is find out if these points are or are not all on the same line.

The easiest way to find if 3 points are or are not on the same line is to find the slope between one pair of points and then find the slope between a different pair of points. If the two slopes are equal then the three points are on the same line. If the slopes are different then the three points are non-collinear.

We'll start with the slope between A and B:
m%5B1%5D+=+%281-%28-2%29%29%2F%28-1-%28-2%29%29+=+3%2F1+=+3
Next the slope between B and C:
m%5B2%5D+=+%284-1%29%2F%281-%28-1%29%29+=+3%2F2
The slopes are different so the points are non-collinear. And three non-collinear points can make a triangle.