# What is the distance between (–4, 0, 2)  and (–1, 4, –2) ?

May 8, 2017

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:

$d = \sqrt{{\left(\textcolor{red}{- 1} - \textcolor{b l u e}{- 4}\right)}^{2} + {\left(\textcolor{red}{4} - \textcolor{b l u e}{0}\right)}^{2} + {\left(\textcolor{red}{- 2} - \textcolor{b l u e}{2}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{- 1} + \textcolor{b l u e}{4}\right)}^{2} + {\left(\textcolor{red}{4} - \textcolor{b l u e}{0}\right)}^{2} + {\left(\textcolor{red}{- 2} - \textcolor{b l u e}{2}\right)}^{2}}$

$d = \sqrt{{3}^{2} + {4}^{2} + {\left(- 4\right)}^{2}}$

$d = \sqrt{9 + 16 + 16}$

$d = \sqrt{41} = 6.403$ rounded to the nearest thousandth