# What is the distance between (1,-10,-3) and (4,3,-2)?

Feb 13, 2017

The distance between the points is $\sqrt{179}$ or $13.379$ rounded to the nearest thousandth.

#### 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:

$d = \sqrt{{\left(\textcolor{red}{4} - \textcolor{b l u e}{1}\right)}^{2} + {\left(\textcolor{red}{3} - \textcolor{b l u e}{- 10}\right)}^{2} + {\left(\textcolor{red}{- 2} - \textcolor{b l u e}{- 3}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{4} - \textcolor{b l u e}{1}\right)}^{2} + {\left(\textcolor{red}{3} + \textcolor{b l u e}{10}\right)}^{2} + {\left(\textcolor{red}{- 2} + \textcolor{b l u e}{3}\right)}^{2}}$

$d = \sqrt{{3}^{2} + {13}^{2} + {1}^{2}}$

$d = \sqrt{9 + 169 + 1}$

$d = \sqrt{179} = 13.379$