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

Jan 24, 2017

The distance is $\sqrt{30}$ or $5.48$ 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:

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

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

$d = \sqrt{{5}^{2} + {\left(- 2\right)}^{2} + {\left(- 1\right)}^{2}}$

$d = \sqrt{25 + 4 + 1}$

$d = \sqrt{30} = 5.48$ rounded to the nearest hundredth