# What is the distance between (5, –6, 4)  and (–10, –2, 2)?

Mar 30, 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:

$d = \sqrt{{\left(\textcolor{red}{- 10} - \textcolor{b l u e}{5}\right)}^{2} + {\left(\textcolor{red}{- 2} - \textcolor{b l u e}{- 6}\right)}^{2} + {\left(\textcolor{red}{2} - \textcolor{b l u e}{4}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{- 10} - \textcolor{b l u e}{5}\right)}^{2} + {\left(\textcolor{red}{- 2} + \textcolor{b l u e}{6}\right)}^{2} + {\left(\textcolor{red}{2} - \textcolor{b l u e}{4}\right)}^{2}}$

$d = \sqrt{{\left(- 15\right)}^{2} + {4}^{2} + {\left(- 2\right)}^{2}}$

$d = \sqrt{225 + 16 + 4}$

$d = \sqrt{245} = 15.652$ rounded to the nearest thousandth.