Question

Find the coordinates of the circumcenter A(3, -1), B(-2, -1), C(3, -8)

Answer 1

\(\large \textit{Centroid of a Triangle}
\begin{array}{llll}
A(x_1,y_1)\quad B(x_2,y_2)\quad C(x_3,y_3)\\ \quad \\
\left(\cfrac{x_1+x_2+x_3}{3}\quad ,\cfrac{y_1+y_2+y_3}{3}\quad \right)
\end{array} \)

Answer 2

The circumcenter of a triangle is the point where the perpendicular bisectors of the three sides intersect. The centroid is the point of intersection of the three medians.

Answer 3

1) Take any pair of two vertices. Using the coordinates of the vertices, find the midpoint. Now find the equation of the perpendicular bisector.
2) Take a different pair of two vertices and do the same.
3) Now you have two equations, each one for the perpendicular bisector of one side.
4) Solve the two equations simultaneously.
5) The solution is the circumcenter.