What are the coordinates of the circumcenter of a triangle with vertices A(−1, 1) , B(5, 1) , and C(−1, −1) ?

This is a right triangle.....the circumcenter will be at the midpoint of the hypotenuse

The endpoints of the hypotenuse are (-1, -1)   and (5, 1)

So  the midpoint - and circumcenter -  is   [ ( 5 - 1) / 2 , (1 - 1 ) / 2 ]  =  ( 2 , 0)