# What is the distance between (7,3,-6) and (-8,1,-1)?

Feb 1, 2017

The distance is $\sqrt{254}$ or $15.94$ 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 gives:

$d = \sqrt{{\left(\textcolor{red}{- 8} - \textcolor{b l u e}{7}\right)}^{2} + {\left(\textcolor{red}{1} - \textcolor{b l u e}{3}\right)}^{2} + {\left(\textcolor{g r e e n}{- 1} - \textcolor{g r e e n}{- 6}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{- 8} - \textcolor{b l u e}{7}\right)}^{2} + {\left(\textcolor{red}{1} - \textcolor{b l u e}{3}\right)}^{2} + {\left(\textcolor{g r e e n}{- 1} + \textcolor{g r e e n}{6}\right)}^{2}}$

$d = \sqrt{{\left(- 15\right)}^{2} + {\left(- 2\right)}^{2} + {\left(5\right)}^{2}}$

$d = \sqrt{225 + 4 + 25}$

$d = \sqrt{254} = 15.94$ rounded to the nearest hundredth