# What is the distance between (3,-29,-12) and (2,-38,-6)?

Mar 7, 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:

$d = \sqrt{{\left(\textcolor{red}{2} - \textcolor{b l u e}{3}\right)}^{2} + {\left(\textcolor{red}{- 38} - \textcolor{b l u e}{- 29}\right)}^{2} + {\left(\textcolor{red}{- 6} - \textcolor{b l u e}{- 12}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{2} - \textcolor{b l u e}{3}\right)}^{2} + {\left(\textcolor{red}{- 38} + \textcolor{b l u e}{29}\right)}^{2} + {\left(\textcolor{red}{- 6} + \textcolor{b l u e}{12}\right)}^{2}}$

$d = \sqrt{{\left(- 1\right)}^{2} + {\left(- 9\right)}^{2} + {6}^{2}}$

$d = \sqrt{1 + 81 + 36}$

$d = \sqrt{118}$

$d = 10.863$ rounded to the nearest thousandth.