Question

Circle O, with center (x, y), passes through the points A(0, 0), B(–3, 0), and C(1, 2). Find the coordinates of the center of the circle. In your final answer, include all formulas and calculations used to find Point O, x, y), the center of circle O.

Answer 1

If it were me, I might be tempted to do this.

1) Pick two pairs of points from AB, AC, BC. It doesn't matter. Just pick two.
2) Find the equation of the line containing the two pairs you picked.
3) Find the midpoint of the line segment containing the two pairs you picked.
4) Find the equation of the perpendicular bisector for each of the two line segments.
5) The intersection of the perpendicular bisectors is the center of the circle.

That sounds about a 1000 times easier from a geometry point of view. Algebra is a little labor-intensive. Good luck!

Answer 2

Okay thank you so much! You're a lifesaver! :)