# What is the distance between (9,-7,1) and (3,-5,-2)?

Feb 14, 2017

The distance is $\sqrt{49}$ or $7$

#### 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:

$d = \sqrt{{\left(\textcolor{red}{3} - \textcolor{b l u e}{9}\right)}^{2} + {\left(\textcolor{red}{- 5} - \textcolor{b l u e}{- 7}\right)}^{2} + {\left(\textcolor{red}{- 2} - \textcolor{b l u e}{1}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{3} - \textcolor{b l u e}{9}\right)}^{2} + {\left(\textcolor{red}{- 5} + \textcolor{b l u e}{7}\right)}^{2} + {\left(\textcolor{red}{- 2} - \textcolor{b l u e}{1}\right)}^{2}}$

$d = \sqrt{{\left(- 6\right)}^{2} + {2}^{2} + {\left(- 3\right)}^{2}}$

d = sqrt((36 + 4 + 9)

$d = \sqrt{49} = 7$