Question

Can someone help me with this

Answer 1

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):

$|AB|=\sqrt{(1+2)^2+(3-5)^2}=\sqrt{13};$

$|BC|=\sqrt(1+1)^2+(3-0)^2}=\sqrt{13};$

$|AC|=\sqrt{(-1+2)^2+(0-5)^2}=\sqrt{26}.$

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.