Question 527594
A (-2,3), B (7,4), and C (5,22)
<pre>
Let's draw the triangle to see what it looks like:

{{{drawing(200,5200/11,-3,8,-2,24,
graph(200,5200/11,-3,8,-2,24),
locate(-2,3,"A(-2,3)"), locate(6,3.5,"B(7,4)"), locate(5.2,22,"C(5,22)"),

triangle(-2,3,7,4,5,22) )}}}

It looks as though angle B could be a right angle which would
make triangle ABC a right triangle.  To find out, we find the
slopes of AB and CB to see if they are opposite-signed reciprocals

To find the slope of AB

m = {{{(y[2]-y[1])/(x[2]-x[1])}}} = {{{(4-3)/(7-(-2))}}} = {{{1/(7+2)}}} = {{{1/9}

To find the slope of CB

m = {{{(y[2]-y[1])/(x[2]-x[1])}}} = {{{(4-22)/(7-5)}}} = {{{(-18)/2}}} = -9

Since the slopes  {{{1/9}}} and -9 are opposite-sign reciprocals
of each other, that is, their product is -1, the lines AB and CB are
perpendicular, and that means that triangle ABC is a right triangle. 

Edwin</pre>