Answer
$2\sqrt{10} \text{ units}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the Distance Formula to find the distance between the given points $\left(
-1,5
\right)$ and $\left(
-7,7
\right)$.
$\bf{\text{Solution Details:}}$
With the given points, then $x_1=
-1
,$ $x_2=
-7
,$ $y_1=
5
,$ and $y_2=
7
.$ 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{(-1-(-7))^2+(5-7)^2}
\\\\
d=\sqrt{(-1+7)^2+(5-7)^2}
\\\\
d=\sqrt{(6)^2+(-2)^2}
\\\\
d=\sqrt{36+4}
\\\\
d=\sqrt{40}
\\\\
d=\sqrt{4\cdot10}
\\\\
d=\sqrt{(2)^2\cdot10}
\\\\
d=2\sqrt{10}
.\end{array}
Hence, the distance is $
2\sqrt{10} \text{ units}
.$
