# What is the distance between (–10, –2, 2) and (4, –4, –2)?

Apr 8, 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:

$d = \sqrt{{\left(\textcolor{red}{4} - \textcolor{b l u e}{- 10}\right)}^{2} + {\left(\textcolor{red}{- 4} - \textcolor{b l u e}{- 2}\right)}^{2} + {\left(\textcolor{red}{- 2} - \textcolor{b l u e}{2}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{4} + \textcolor{b l u e}{10}\right)}^{2} + {\left(\textcolor{red}{- 4} + \textcolor{b l u e}{2}\right)}^{2} + {\left(\textcolor{red}{- 2} - \textcolor{b l u e}{2}\right)}^{2}}$

$d = \sqrt{{14}^{2} + {\left(- 2\right)}^{2} + {\left(- 4\right)}^{2}}$

$d = \sqrt{196 + 4 + 16}$

$d = \sqrt{216} = 14.697$ rounded to the nearest thousandth.