The center of the circle is the same as the midpoint of its diameter.
To find the coordinates of the midpoint of a segment, calculate the average between the x and y coordinates of the endpoints of the segment, respectively.
The x-coordinate of the point S is 6 and that of the point W is 10. Then, the average between those values, is:
[tex]\frac{6+10}{2}=\frac{16}{2}=8[/tex]Similarly, since the y-coordinate of the point S is -1 and that of the point W is -7, then the average of the y-coordinates is:
[tex]\frac{-1-7}{2}=\frac{-8}{2}=-4[/tex]Therefore, the coordinates of the center of the circle are:
[tex](8,-4)[/tex]
