# What is the distance between (8,3,-5) and (6,1,2)?

Jan 18, 2017

The distance between the points is $d = \sqrt{57}$ or $d = 7.55$ 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 problem gives:

$d = \sqrt{{\left(\textcolor{red}{6} - \textcolor{b l u e}{8}\right)}^{2} + {\left(\textcolor{red}{1} - \textcolor{b l u e}{3}\right)}^{2} + {\left(\textcolor{g r e e n}{2} - \textcolor{g r e e n}{- 5}\right)}^{2}}$

$d = \sqrt{{\left(- 2\right)}^{2} + {\left(- 2\right)}^{2} + {\left(7\right)}^{2}}$

$d = \sqrt{4 + 4 + 49}$

$d = \sqrt{57} = 7.55$ rounded to the nearest hundredth