Answer
The distance between the pair of points $\left( -4,3 \right)$ and $\left( -2,5 \right)$ is $2.83$ units.
Work Step by Step
Consider the provided pair of points:
$\left( -4,3 \right)$ and $\left( -2,5 \right)$
The distance $d$, between the points $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ is given by:
$d=\sqrt{{{\left( {{x}_{2}}-{{x}_{1}} \right)}^{2}}+{{\left( {{y}_{2}}-{{y}_{1}} \right)}^{2}}}$
Substitute $-2$ for ${{x}_{2}}$, $-4$ for ${{x}_{1}}$, $5$ for ${{y}_{2}}$ and $3$ for ${{y}_{1}}$ in the above formula and simplify:
$\begin{align}
& d=\sqrt{{{\left( -2-\left( -4 \right) \right)}^{2}}+{{\left( 5-3 \right)}^{2}}} \\
& =\sqrt{{{\left( 2 \right)}^{2}}+{{\left( 2 \right)}^{2}}} \\
& =\sqrt{4+4} \\
& =\sqrt{8}
\end{align}$
On further simplification,
$\begin{align}
& d=2\sqrt{2} \\
& \approx 2.83
\end{align}$
Therefore, the distance between the pair of points $\left( -4,3 \right)$ and $\left( -2,5 \right)$ is $2.83$ units.
