# To the nearest tenth, what is the distanc between the points (5, 12, 7) and (8, 2, 10)?

Jun 28, 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:

$d = \sqrt{{\left(\textcolor{red}{8} - \textcolor{b l u e}{5}\right)}^{2} + {\left(\textcolor{red}{2} - \textcolor{b l u e}{12}\right)}^{2} + {\left(\textcolor{red}{10} - \textcolor{b l u e}{7}\right)}^{2}}$

$d = \sqrt{{3}^{2} + {\left(- 10\right)}^{2} + {3}^{2}}$

$d = \sqrt{9 + 100 + 9}$

$d = \sqrt{118}$

$d = 10.9$ rounded to the nearest tenth.