Question

What are the coordinates of the center of the circle that passes through the points (1, 1), (1, 5), and (5, 5)?

Answer 1

`(3, 3)`

Explanation:

Along with the point `(5, 1)` these points are the vertices of a square, so the centre of the circle will be at the midpoint of the diagonal between `(1, 1)` and `(5, 5)`, that is:

`((1+5)/2, (1+5)/2) = (3,3)`

The radius is the distance between `(1, 1)` and `(3, 3)`, that is:

`sqrt((3-1)^2+(3-1)^2) = sqrt(8)`

So the equation of the circle may be written:

`(x-3)^2+(y-3)^2 = 8`

graph{((x-3)^2+(y-3)^2-8)((x-3)^2+(y-3)^2-0.01)((x-1)^2+(y-1)^2-0.01)((x-5)^2+(y-1)^2-0.01)((x-1)^2+(y-5)^2-0.01)((x-5)^2+(y-5)^2-0.01)((x-3)^100+(y-3)^100-2^100)(x-y)(sqrt(17-(x+y-6)^2)/sqrt(17-(x+y-6)^2)) = 0 [-5.89, 9.916, -0.82, 7.08]}