# What is the distance between (–6, 3, 4)  and (4, –4, –2)?

Mar 10, 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:

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

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

$d = \sqrt{{10}^{2} + {\left(- 7\right)}^{2} + {\left(- 6\right)}^{2}}$

$d = \sqrt{100 + 49 + 36}$

$d = \sqrt{185}$

Or

$d = 13.601$ rounded to the nearest thousandth