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
[tex]9\frac{-2-2}{2},\frac{-2-5}{2}) = (-2, -3.5)[/tex]
So, the equation of perpendicular line of AB would have slope 0 and it would be
y=-3.5.
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
[tex](\frac{-2+7}{2},\frac{-5-5}{2}) = (2.5, -5)[/tex]
So, the equation of perpendicular line of AC would have slope undefined and it would be
x=2.5.
So, the intersection point of lines x=2.5 and y=-3.5 is (2.5, -3.5).
Therefore, the circumcenter of the triangle is (2.5, -3.5).
