Answer
$\text{a) Distance: }
\sqrt{202}
\text{ units}\\\text{b) Midpoint: }
\left( -\dfrac{5}{2}, -\dfrac{1}{2} \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the Distance Formula and the Midpoint Formula to find the distance and the midpoint of the given points $\left(
-8,4
\right)$ and $\left(
3,-5
\right).$
$\bf{\text{Solution Details:}}$
With the given points, then $x_1=
-8
,$ $x_2=
3
,$ $y_1=
4
,$ and $y_2=
-5
.$
Using the Distance Formula which is given by $d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}
,$ then
\begin{array}{l}\require{cancel}
d=\sqrt{(-8-3)^2+(4-(-5))^2}
\\\\
d=\sqrt{(-8-3)^2+(4+5)^2}
\\\\
d=\sqrt{(-11)^2+(9)^2}
\\\\
d=\sqrt{121+81}
\\\\
d=\sqrt{202}
.\end{array}
Using $\left( \dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2} \right)$ or the Midpoint Formula, then the midpoint of the line segment with endpoints given above is
\begin{array}{l}\require{cancel}
\left( \dfrac{-8+3}{2}, \dfrac{4+(-5)}{2} \right)
\\\\=
\left( \dfrac{-8+3}{2}, \dfrac{4-5}{2} \right)
\\\\=
\left( \dfrac{-5}{2}, \dfrac{-1}{2} \right)
\\\\=
\left( -\dfrac{5}{2}, -\dfrac{1}{2} \right)
.\end{array}
Hence,
$
\text{a) Distance: }
\sqrt{202}
\text{ units}\\\text{b) Midpoint: }
\left( -\dfrac{5}{2}, -\dfrac{1}{2} \right)
.$