What are the coordinates of the circumcenter of the triangle? show your work < 3

We need to find the Circumcenter of the triangle.

Circumcenter could be found by drawing perpendicular bisector of two segments of a triangle.

We have AB a vertical line. So the slope of the vertical line is undefine and slope of perpendicular line to that line would be 0.

We need to find a mid-point between A and B points.

The coordinates of A and B are

A( -2,-5) and B(-2,-2).

So, the Midpoint would be

So, the equation of perpendicular line of AB would have slope 0 and it would be

Now, let us find perpendicular bisector line of AC.

We have coordinates of A and C points as

A(-2,-5) and C(7,-5)

So, the Midpoint would be

So, the equation of perpendicular line of AC would have slope undefined and it would be

So, the intersection point of lines x=2.5 and y=-3.5 is (2.5, -3.5).

the answer is a

step-by-step explanation: