# What is the distance between (3,-4,15) and (12,-11,6)?

Mar 11, 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:

$d = \sqrt{{\left(\textcolor{red}{12} - \textcolor{b l u e}{3}\right)}^{2} + {\left(\textcolor{red}{- 11} - \textcolor{b l u e}{- 4}\right)}^{2} + {\left(\textcolor{red}{6} - \textcolor{b l u e}{15}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{12} - \textcolor{b l u e}{3}\right)}^{2} + {\left(\textcolor{red}{- 11} + \textcolor{b l u e}{4}\right)}^{2} + {\left(\textcolor{red}{6} - \textcolor{b l u e}{15}\right)}^{2}}$

$d = \sqrt{{9}^{2} + {\left(- 7\right)}^{2} + {\left(- 9\right)}^{2}}$

$d = \sqrt{81 + 49 + 81}$

$d = \sqrt{211}$

Or

$d = 14.526$ rounded to the nearest thousandth.