SOLUTION: A triangle with vertices (3, −2), (7, 3), and (−7, 6) is what type of triangle?

We draw the triangle to see what it looks like:

 (3, -2), (7, 3), and (-7, 6) 



Looks suspiciously like the angle down at (3,-2) is a right
angle.   So let's see if we can prove that it is.

We find the slopes of its two sides and if that's a right angle 
then the slope of one with be the reciprocal of the other with
the opposite sign

We use the slope formula:


where (x1,y1) = (-7,6)
and where (x2,y2) = (3,-2)




We use the slope formula again:


this time with (x1,y1) = (7,3)
and where (x2,y2) = (3,-2)




Indeed  and  are reciprocals with
opposite signs, so the sides are perpendicular and
the angle with vertex (3,-2) is a right angle.

So the triangle is a right triangle.

Edwin