# What is the distance between (3, –1, 1)  and (6, 0, 4) ?

Mar 5, 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:

$d = \sqrt{{\left(\textcolor{red}{6} - \textcolor{b l u e}{3}\right)}^{2} + {\left(\textcolor{red}{0} - \textcolor{b l u e}{- 1}\right)}^{2} + {\left(\textcolor{red}{4} - \textcolor{b l u e}{1}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{6} - \textcolor{b l u e}{3}\right)}^{2} + {\left(\textcolor{red}{0} + \textcolor{b l u e}{1}\right)}^{2} + {\left(\textcolor{red}{4} - \textcolor{b l u e}{1}\right)}^{2}}$

$d = \sqrt{{3}^{2} + {1}^{2} + {3}^{2}}$

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

$d = \sqrt{19}$

Or

$d = 4.359$ rounded to the nearest thousandth.