Question

The vertices of triangle ABC are A(1,1), B(0,2), and C(3,-2). Find the coordinates of the circumcenter.

Answer 1

The circumcenter is the intersection of the perpendicular bisectors of the sides. So we need to find the equations of 2 of the perpendicular bisectors and figure out where they intersect.
Or you might try a graphical solution.

Answer 2

The circumcenter is the place where the right bisectors intersect. So you you have to do the following:
1. Determine a midpoint on a line (say AB)
2. Determine an equation for a line perpendicular to AB that passes through that midpoint you found in (1)
3. Repeat steps 1&2 for another bisector
4. If you equate the two equations together (say they are equal) you can then solve for x in order to find out the x value of the intersection point