Question

What are the coordinates of the circumcenter of the triangle?

Answer 1

It's the right angle. The circumcenter is in half of hypotenuse.

The formula of a midpoint of segment BC:

$M\left(\dfrac{x_B+x_C}{2},\ \dfrac{y_B+y_C}{2}\right)$

We have the points B(-2, -2) and C(7, -5). Substitute:

$\dfrac{-2+7}{2}=\dfrac{5}{2}=2.5\\\\\dfrac{-2+(-5)}{2}=\dfrac{-7}{2}=-3.5$

Answer: (2.5, -3.5)