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Find the circumcenter of a triangle that has these points

A=(4,5)

B=(-8,-6)

C=(4,-6)

find the midd point between A and B

The circumcenter of a right triangle is the midd point between A and B (Thales' theorem).

M is the midd point between A and B.

\(\begin{array}{rcll} \vec{M} &=& \frac12\cdot \left[ \vec{A} + \vec{B} \right]\\ \vec{M} &=& \frac12\cdot \left[ \binom{4}{5} + \binom{-8}{-6} \right]\\ \vec{M} &=& \frac12\cdot \left[ \binom{4-8}{5-6} \right]\\ \vec{M} &=& \frac12\cdot \left[ \binom{-4}{-1}\right]\\ \vec{M} &=& \dbinom{ -\frac{4}{2} } {-\frac{1}{2} }\\ \vec{M} &=& \binom{-2}{-0.5} \\ \end{array}\)

The circumcenter of a right triangle is (-2, -0.5)