# What is the distance between  (–2, 1, 3)  and (–1, 2, –3) ?

Feb 12, 2017

The distance between the points is $\sqrt{11}$ or $3.317$ rounded to the nearest thousandth.

#### 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:

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

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

$d = \sqrt{{1}^{2} + {1}^{2} + {\left(- 3\right)}^{2}}$

$d = \sqrt{1 + 1 + 9}$

$d = \sqrt{11} = 3.317$ rounded to the nearest thousandth.