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 of the circle is `("-"1,2)`

Explanation:

The center of a circle is the midpoint of its diameter.

The midpoint of a line segment is given by the formula `(x_"mid",y_"mid")=((x_("end"1)+x_("end"2))/2,(y_("end"1)+y_("end"2))/2)`.

Plugging in the coordinates of the endpoints gives `(x_"mid",y_"mid")=(("-"7+5)/2,(3+1)/2)=(("-"2)/2,4/2)=("-1",2)`.