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

Mar 27, 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:

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

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

$d = \sqrt{{\left(- 6\right)}^{2} + {\left(3\right)}^{2} + {\left(- 4\right)}^{2}}$

$d = \sqrt{36 + 9 + 16}$

$d = \sqrt{45 + 16}$

$d = \sqrt{61}$

Or

$d \approx 7.81$