Question

Find the center of the circle with these three points: (-4,3), (3,10), and (10,3). Separate the coordinates with a comma.

Answer 1

If we plot these, we can see that the far left and far right coordinates are exactly 14 units away (in x direction) this is the diameter.

therefore our radious of this circle will be 7 units. So our x coordinate of the centre will be -4 +7 or 10-7 which is 3.
And so our y coordinate will be 10-7 = 3 too.

Centre is at (3, 3)

Answer 2

(y coordinate was found by subtracting radius from the upper point on the circle in the y direction, i.e. the 10 in (3, 10)

Answer 3

The equation of a circle is given by:
\[(x-h)^2+(y-k)^2=r^2\].
You can plug in the coordinates 3 times. Then you have 3 equations and 3 unknowns. Solve for h,k. That is the coords for the center.
What ggabnore said is true^^
My approach is more analytic/algebraic.