# What is the distance between (-13,13,-4) and (-1,-6,-2)?

Mar 9, 2018

See a 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:

$d = \sqrt{{\left(\textcolor{red}{- 1} - \textcolor{b l u e}{- 13}\right)}^{2} + {\left(\textcolor{red}{- 6} - \textcolor{b l u e}{13}\right)}^{2} + {\left(\textcolor{red}{- 2} - \textcolor{b l u e}{- 4}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{- 1} + \textcolor{b l u e}{13}\right)}^{2} + {\left(\textcolor{red}{- 6} - \textcolor{b l u e}{13}\right)}^{2} + {\left(\textcolor{red}{- 2} + \textcolor{b l u e}{4}\right)}^{2}}$

$d = \sqrt{{12}^{2} + {\left(- 19\right)}^{2} + {2}^{2}}$

$d = \sqrt{144 + 361 + 4}$

$d = \sqrt{509}$

Or

$d = 22.561$ rounded to the nearest thousandth