Answer
Right triangle
Work Step by Step
Determine the length of each side using the formula
$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$,
where $(x_1,y_1),(x_2,y_2)$ are the coordinates of the two points.
$d_1=\sqrt{(4-2)^2+(0-1)^2}=\sqrt 5$
$d_2=\sqrt{[4-(-1)]^2+[0-(-5)]^2}=\sqrt{50}=5\sqrt 2$
$d_3=\sqrt{[2-(-1)]^2+[1-(-5)]^2}=\sqrt{45}=3\sqrt 5$
Compute $d_1^2+d_3^2$:
$d_1^2+d_3^2=(\sqrt 5)^2+(3\sqrt 5)^2=5+45=50$
Compute $d_2^2$:
$d_2^2=(5\sqrt 2)^2=50$
As $d_1^2+d_3^2=d_2^2$, the three sides verify the Pythagorean Theorem, so the triangle is a right triangle.
