Chapter 9 Quadratic Relations and Conic Sections - 9.3 Graph and Write Equations of Circles - 9.3 Exercises - Quiz for Lessons 9.1-9.3 - Page 632: 1

See below.

The distance formula from $P_1(x_1,y_1)$ to $P_2(x_2,y_2)$ is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. The midpoint $M$ of the line segment from $P_1(x_1,y_1)$ to $P_2(x_2,y_2)$ is: $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$. Hence: $d=\sqrt{(4-8)^2+(-3-(-7))^2}=\sqrt{16+16}=\sqrt{32}=4\sqrt2.$ $M=(\frac{4+8}{2},\frac{-3+(-7)}{2})=(6,-5)$.