# How do you find the distance between (-10,8) and (2,-3)?

Apr 7, 2017

See the entire solution process below:

#### Explanation:

The formula for calculating the distance between two points is:

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

Substituting the values from the points in the problem gives:

$d = \sqrt{{\left(\textcolor{red}{2} - \textcolor{b l u e}{- 10}\right)}^{2} + {\left(\textcolor{red}{- 3} - \textcolor{b l u e}{8}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{2} + \textcolor{b l u e}{10}\right)}^{2} + {\left(\textcolor{red}{- 3} - \textcolor{b l u e}{8}\right)}^{2}}$

$d = \sqrt{{12}^{2} + {\left(- 11\right)}^{2}}$

$d = \sqrt{144 + 121}$

$d = \sqrt{265} = 16.279$ rounded to the nearest thousandth.