Answer
$\text{a) Distance: }
2\sqrt{17}
\text{ units}\\\text{b) Midpoint: }
\left( 5,2 \right)$
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 $\left(
6,-2
\right)$ and $\left(
4,6
\right).$
$\bf{\text{Solution Details:}}$
With the given points, then $x_1=
6
,$ $x_2=
4
,$ $y_1=
-2
,$ and $y_2=
6
.$
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{(6-4)^2+(-2-6)^2}
\\\\
d=\sqrt{(2)^2+(-8)^2}
\\\\
d=\sqrt{4+64}
\\\\
d=\sqrt{68}
\\\\
d=\sqrt{4\cdot17}
\\\\
d=\sqrt{(2)^2\cdot17}
\\\\
d=2\sqrt{17}
.\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{6+4}{2}, \dfrac{-2+6}{2} \right)
\\\\=
\left( \dfrac{10}{2}, \dfrac{4}{2} \right)
\\\\=
\left( 5,2 \right)
.\end{array}
Hence,
$
\text{a) Distance: }
2\sqrt{17}
\text{ units}\\\text{b) Midpoint: }
\left( 5,2 \right)
.$