Answer:
The circumcenter is (-1 , -6.5)
Explanation:
the circumcenter is the point where the perpendicular bisectors of a triangle intersects.
See the attached figure
A(-6, - 8), B(4. – 5), C(-6,-5).
As shown at the graph ΔABC is aright triangle at C
The perpendicular bisector of AC is the line y =-6.5
The perpendicular bisector of BC is the line x = -1
The intersection between y =-6.5 and x = -1 will be the point (-1,-6.5)
So, The circumcenter is (-1 , -6.5)
Another solution:
As the graph represents a right triangle.
The circumcenter of a right triangle lies exactly at the midpoint of the hypotenuse
The hypotenuse is the line segment AB
The midpoint of AB = (A + B)/2 = [(-6, - 8) +(4. – 5)]/2 = (-2,-13)/2 = (-1 , -6.5)
So, The circumcenter is (-1 , -6.5)