Step-by-step explanation:
if the vertex A is (-2;5), vertex B is (1;3) and the vertex C is (-1;0), then
1) the lengths are (note, the side AC should be hypotenuse):
[tex]|AB|=\sqrt{(1+2)^2+(3-5)^2}=\sqrt{13};[/tex]
[tex]|BC|=\sqrt(1+1)^2+(3-0)^2}=\sqrt{13};[/tex]
[tex]|AC|=\sqrt{(-1+2)^2+(0-5)^2}=\sqrt{26}.[/tex]
2) if to check the equation AB²+BC²=AC², then
13+13=26 - it is true.
It means, the triangle ΔABC is right triangle.
P.S. all the details are in the attachment.
