Chapter 9 Quadratic Relations and Conic Sections - 9.1 Apply the Distance and Midpoint Formulas - 9.1 Exercises - Skill Practice - Page 617: 9

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: $d=\sqrt{(-4-8)^2+(8-(-4))^2}=\sqrt{144+144}=\sqrt{288}=12\sqrt2.$ $M=(\frac{-4+8}{2},\frac{8+(-4)}{2})=(2,2)$.