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

Feb 25, 2017

The distance between the two points is $\sqrt{86}$ or $9.274$ rounded to the nearest hundredth

#### 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:

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

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

$d = \sqrt{{\left(- 6\right)}^{2} + {7}^{2} + {\left(- 1\right)}^{2}}$

$d = \sqrt{36 + 49 + 1}$

$d = \sqrt{86} = 9.274$ rounded to the nearest hundredth