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

1 Answer
Jan 30, 2016

Answer:

#(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]}