# What is the distance between (13,23,-10) and (-3,17,-22)?

Apr 11, 2017

See the entire solution process below:

#### Explanation:

The formula for calculating the distance between two points is:

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

Substituting the values from the points in the problem gives:

$d = \sqrt{{\left(\textcolor{red}{- 3} - \textcolor{b l u e}{13}\right)}^{2} + {\left(\textcolor{red}{17} - \textcolor{b l u e}{23}\right)}^{2} + {\left(\textcolor{red}{- 22} - \textcolor{b l u e}{- 10}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{- 3} - \textcolor{b l u e}{13}\right)}^{2} + {\left(\textcolor{red}{17} - \textcolor{b l u e}{23}\right)}^{2} + {\left(\textcolor{red}{- 22} + \textcolor{b l u e}{10}\right)}^{2}}$

$d = \sqrt{{\left(- 16\right)}^{2} + {\left(- 6\right)}^{2} + {\left(- 12\right)}^{2}}$

$d = \sqrt{256 + 36 + 144}$

$d = \sqrt{436} = 20.881$ rounded to the nearest thousandth.