The center is the midpoint of the diameter.
The coordinates of the midpoint if the endpoints are (x₁,y₁) and (x₂,y₂):
[tex](\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]
[tex](-7,3) \\
x_1=-7 \\ y_1=3 \\ \\
(5,1) \\
x_2=5 \\ y_2=1 \\ \\
\frac{x_1+x_2}{2}=\frac{-7+5}{2}=\frac{-2}{2}=-1 \\
\frac{y_1+y_2}{2}=\frac{3+1}{2}=\frac{4}{2}=2 \\ \\
\boxed{\hbox{the center: } (-1,2)}[/tex]
The answer is C.
