A circle passes through the points (-2,0), (2,0), and (3,2). Find the center of the circle. Enter your answer as an ordered pair.
Thank you
The center is the point where the perpendicular bisectors of two chords intersect.
Plan: to find the equations of the two perpendicular bisectors and then find what point they have in common.
The first chord has endpoints (-2,0) and (2,0). This chord is horizontal and has a midpoint of (0,0).
The perpendicular bisector will be the y-axis and the y-axis has an equation of x = 0.
The second chord has endpoints (2,0) and (3,2). This chord has its midpoint at (2.5,1).
The slope of this chord is: (2 - 0)/(3 -2 ) = 2. Therefore, the slope of the perpendicular bisector is -1/2.
The equation of the perpendicular bisector is: y - 1 = -0.5(x - 2.5)
Simplifying this equation gives: 2x + 4y = 9.
The point where x = 0 and 2x + 3y = 9 intersect is: (0, 2.25)