Question

Find the circumcenter of the triangle ABC.

Answer 1

Answer:

The circumcenter is (-1 , -6.5)

Step-by-step 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)