To find the distance and the midpoint between those points, we just need to use the distance formula and the midpoint formula. The distance formula is
[tex]d((x_1,y_1,z_1),(x_2,y_2,z_2))=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}[/tex]
and the midpoint formula is
[tex]M((x_1,y_1,z_1),(x_2,y_2,z_2))=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2},\frac{z_1+z_2}{2})[/tex]
Using those formulas in our problem, for the distance we have
[tex]\begin{gathered} d((-3_{},0,-7),(-8,-9,-11)) \\ =\sqrt[]{((-8)-(-3))^2+((-9)-(0))^2+((-11)-(-7))^2} \\ =\sqrt[]{(-8+3)^2+(-9-0)^2+(-11+7)^2} \\ =\sqrt[]{(5)^2+(-9)^2+(-4)^2} \\ =\sqrt[]{25+81+16} \\ =11.0453610172\ldots\approx11.0 \end{gathered}[/tex]
and for the Midpoint, we have
[tex]\begin{gathered} M((-3_{},0,-7),(-8,-9,-11)) \\ =(\frac{(-3)+(-8)_{}}{2},\frac{(0)+(-9)}{2},\frac{(-7)+(-11)_{}}{2}) \\ =(\frac{-3-8}{2},\frac{0-9}{2},\frac{-7-11_{}}{2}) \\ =(\frac{-11}{2},\frac{-9}{2},\frac{-18_{}}{2}) \\ =(-5.5,-4.5,-9) \end{gathered}[/tex]
And those are our answers.
[tex]\begin{cases}d\approx11 \\ M(-5.5,-4.5,-9)\end{cases}[/tex]
