# How do you find the distance between (-6,-2) and (-7,-5)?

Mar 19, 2017

$= \sqrt{10}$

#### Explanation:

We use the distance formula: $\sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$

Lets label our points for easier classification:
$\left(\textcolor{b l u e}{- 6} , \textcolor{red}{- 2}\right) \to \left(\textcolor{b l u e}{{x}_{1}} , \textcolor{red}{{y}_{1}}\right)$
$\left(\textcolor{b l u e}{- 7} , \textcolor{red}{- 5}\right) \to \left(\textcolor{b l u e}{{x}_{2}} , \textcolor{red}{{y}_{2}}\right)$

Now we can substitute in for the distance formula:
$\sqrt{{\textcolor{b l u e}{\left(- 7 - \left(- 6\right)\right)}}^{2} + {\textcolor{red}{\left(- 5 - \left(- 2\right)\right)}}^{2}}$

$= \sqrt{{\textcolor{b l u e}{\left(- 1\right)}}^{2} + {\textcolor{red}{\left(- 3\right)}}^{2}}$

$= \sqrt{\textcolor{b l u e}{\left(1\right)} + \textcolor{red}{\left(9\right)}}$

$= \sqrt{10}$