# What is the distance between (-2,1,14) and (-12,2,-5)?

May 22, 2017

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:

$d = \sqrt{{\left(\textcolor{red}{- 12} - \textcolor{b l u e}{- 2}\right)}^{2} + {\left(\textcolor{red}{2} - \textcolor{b l u e}{1}\right)}^{2} + {\left(\textcolor{red}{- 5} - \textcolor{b l u e}{14}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{- 12} + \textcolor{b l u e}{2}\right)}^{2} + {\left(\textcolor{red}{2} - \textcolor{b l u e}{1}\right)}^{2} + {\left(\textcolor{red}{- 5} - \textcolor{b l u e}{14}\right)}^{2}}$

$d = \sqrt{{\left(- 10\right)}^{2} + {1}^{2} + {\left(- 19\right)}^{2}}$

$d = \sqrt{100 + 1 + 361}$

$d = \sqrt{462}$

$d = 21.494$ rounded to the nearest thousandth.