# What is the distance between (-7,-6,4) and (-2,3,4)?

Sep 29, 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:

$d = \sqrt{{\left(\textcolor{red}{- 2} - \textcolor{b l u e}{- 7}\right)}^{2} + {\left(\textcolor{red}{3} - \textcolor{b l u e}{- 6}\right)}^{2} + {\left(\textcolor{red}{4} - \textcolor{b l u e}{4}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{- 2} + \textcolor{b l u e}{7}\right)}^{2} + {\left(\textcolor{red}{3} + \textcolor{b l u e}{6}\right)}^{2} + {\left(\textcolor{red}{4} - \textcolor{b l u e}{4}\right)}^{2}}$

$d = \sqrt{{5}^{2} + {9}^{2} + {0}^{2}}$

$d = \sqrt{25 + 81 + 0}$

$d = \sqrt{106}$

Or, if you need a single number:

$d = 10.296$ rounded to the nearest thousandth