# What is the distance between (2,1,-7) and (1,5,3)?

Apr 8, 2017

See the entire 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:

$d = \sqrt{{\left(\textcolor{red}{1} - \textcolor{b l u e}{2}\right)}^{2} + {\left(\textcolor{red}{5} - \textcolor{b l u e}{1}\right)}^{2} + {\left(\textcolor{red}{3} - \textcolor{b l u e}{- 7}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{1} - \textcolor{b l u e}{2}\right)}^{2} + {\left(\textcolor{red}{5} - \textcolor{b l u e}{1}\right)}^{2} + {\left(\textcolor{red}{3} + \textcolor{b l u e}{7}\right)}^{2}}$

$d = \sqrt{{\left(- 1\right)}^{2} + {4}^{2} + {10}^{2}}$

$d = \sqrt{1 + 16 + 100}$

$d = \sqrt{117} = 10.817$ rounded to the nearest thousandth.