Question

The endpoints of the diameter of a circle are (-7, 3) and (5, 1). What is the center of the circle?

Answer 1

The center is the midpoint of the diameter.

The coordinates of the midpoint if the endpoints are (x₁,y₁) and (x₂,y₂):
$(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

$(-7,3) \\ x_1=-7 \\ y_1=3 \\ \\ (5,1) \\ x_2=5 \\ y_2=1 \\ \\ \frac{x_1+x_2}{2}=\frac{-7+5}{2}=\frac{-2}{2}=-1 \\ \frac{y_1+y_2}{2}=\frac{3+1}{2}=\frac{4}{2}=2 \\ \\ \boxed{\hbox{the center: } (-1,2)}$

The answer is C.