# What is the distance between (5, –6, 4)  and (–5, –1, 1)?

Jan 16, 2017

$d = \sqrt{134}$

Or

$d = 11.6$ rounded to the nearest tenth.

#### Explanation:

The formula for calculating the distance between two points is:

$d = \sqrt{{\left(\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}\right)}^{2} + {\left(\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}\right)}^{2} + {\left(\textcolor{g r e e n}{{z}_{2}} - \textcolor{g r e e n}{{z}_{1}}\right)}^{2}}$

Substituting the two points from the problem and solving gives:

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

$d = \sqrt{{\left(- 10\right)}^{2} + {\left(5\right)}^{2} + {\left(- 3\right)}^{2}}$

$d = \sqrt{100 + 25 + 9}$

$d = \sqrt{134}$

Or

$d = 11.6$ rounded to the nearest tenth.