Answer
$$a^2+b^2=(5)^2+(12)^2 = 169\\c^2 = (13)^2=169$$
$\therefore a^2+b^2 = c^2 $ and the triangle is a right triangle.
Work Step by Step
To find $a,b$ and $c$, we use the distance formula
$$r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\a=\sqrt{(5-0)^2+(0-0)^2}=5\\b=\sqrt{(5-5)^2+(12-0)^2}=12\\ c=\sqrt{(5-0)^2+(12-0)^2}=13$$
$$a^2+b^2=(5)^2+(12)^2 = 169\\c^2 = (13)^2=169$$
$\therefore a^2+b^2 = c^2 $ and the triangle is a right triangle.
