# What is the distance between (3,-14,15) and (12,-21,16)?

Apr 27, 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:

$d = \sqrt{{\left(\textcolor{red}{12} - \textcolor{b l u e}{3}\right)}^{2} + {\left(\textcolor{red}{- 21} - \textcolor{b l u e}{- 14}\right)}^{2} + {\left(\textcolor{red}{16} - \textcolor{b l u e}{15}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{12} - \textcolor{b l u e}{3}\right)}^{2} + {\left(\textcolor{red}{- 21} + \textcolor{b l u e}{14}\right)}^{2} + {\left(\textcolor{red}{16} - \textcolor{b l u e}{15}\right)}^{2}}$

$d = \sqrt{{9}^{2} + {\left(- 7\right)}^{2} + {1}^{2}}$

$d = \sqrt{81 + 49 + 1}$

$d = \sqrt{131}$

Or

$d \cong 11.45$