# What is the distance between (8,-4,6) and (-1,-3,5)?

Mar 13, 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:

$d = \sqrt{{\left(\textcolor{red}{- 1} - \textcolor{b l u e}{8}\right)}^{2} + {\left(\textcolor{red}{- 3} - \textcolor{b l u e}{- 4}\right)}^{2} + {\left(\textcolor{red}{5} - \textcolor{b l u e}{6}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{- 1} - \textcolor{b l u e}{8}\right)}^{2} + {\left(\textcolor{red}{- 3} + \textcolor{b l u e}{4}\right)}^{2} + {\left(\textcolor{red}{5} - \textcolor{b l u e}{6}\right)}^{2}}$

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

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

$d = \sqrt{83}$

Or

$d = 9.110$ rounded to the nearest thousandth.