Question 401043
<i>Any</i> 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.<br>
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.<br>
We'll start with the slope between A and B:
{{{m[1] = (1-(-2))/(-1-(-2)) = 3/1 = 3}}}
Next the slope between B and C:
{{{m[2] = (4-1)/(1-(-1)) = 3/2}}}
The slopes are different so the points are non-collinear. And three non-collinear points can make a triangle.