Answer
The line through $P_{1}=(-2,5),P_{2}=(1,3) $ has slope
$m_{12}=\displaystyle \frac{5-3}{-2-1}=\frac{2}{-3}=-\frac{2}{3}$
The line through $P_{2}=(1,3),P_{3}=(-1,0) $ has slope
$m_{23}=\displaystyle \frac{3-0}{1-(-1)}=\frac{3}{2}$
Since $m_{12}\cdot m_{23}=-1 ,$
the sides $\overline{P_{1}P_{2}}$ and $\overline{P_{2}P_{3}}$ are perpendicular,
and the triangle $\triangle P_{1}P_{2}P_{3}$ is a right triangle,
Work Step by Step
All steps are given in the answer.
We used the Criterion for Perpendicular Lines:
Two nonvertical lines are perpendicular if and only if the product of their slopes is $-1.$
