Question

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

a. (-6,2)
b. (-2,4)
c. (-1,2)

Answer 1

c. (-1,2)

Explanation:

Answer 2

The center is the midpoint of the diameter.

The coordinates of the midpoint if the endpoints are (x₁,y₁) and (x₂,y₂):

`((x_1+x_2)/(2), (y_1+y_2)/(2))`


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

The answer is C.