Answer
$\color{blue}{\bf{ \sqrt{85} \text{ ; } (-\dfrac{1}{2},2) }}$
Work Step by Step
We are given the two points, $P(3, -1), Q(-4, 5)$, and asked to find the distance between them.
We'll use the distance formula:
$d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$
$d=\sqrt{(3-(-4))^2+(-1-5)^2}$
$d=\sqrt{7^2+(-6)^2}$
$d=\sqrt{49+36}$
$d=\color{blue}{\bf{ \sqrt{85} }}$
We are also asked to find the midpoint between $P$ and $Q$
We'll use the midpoint formula:
$m=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})$
$m=(\dfrac{3+(-4)}{2},\dfrac{-1+5}{2})$
$m=(\dfrac{-1}{2},\dfrac{4}{2})$
$m=\color{blue}{\bf{ (-\dfrac{1}{2},2) }}$
