# What is the distance between (0, 0, 8)  and (6, 8, 2) ?

Jan 21, 2017

The distance between the points is $\sqrt{136}$ or $11.66$ rounded to the nearest hundredth

#### Explanation:

The formula for calculating the distance between two points is:

$d = \sqrt{{\left(\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}\right)}^{2} + {\left(\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}\right)}^{2} + {\left(\textcolor{g r e e n}{{z}_{2}} - \textcolor{g r e e n}{{z}_{1}}\right)}^{2}}$

Substituting the values from the points in the problem and calculating for $d$ gives:

$d = \sqrt{{\left(\textcolor{red}{6} - \textcolor{b l u e}{0}\right)}^{2} + {\left(\textcolor{red}{8} - \textcolor{b l u e}{0}\right)}^{2} + {\left(\textcolor{g r e e n}{2} - \textcolor{g r e e n}{8}\right)}^{2}}$

$d = \sqrt{{\left(6\right)}^{2} + {\left(8\right)}^{2} + {\left(- 6\right)}^{2}}$

$d = \sqrt{36 + 64 + 36}$

$d = \sqrt{136} = 11.66$ rounded to the nearest hundredth