# What is the distance between (–6, 3, 1)  and (2, –3, 1) ?

Apr 18, 2017

$10 \text{ units}$

#### Explanation:

using the 3-d version of the $\textcolor{b l u e}{\text{distance formula}}$

color(red)(bar(ul(|color(white)(2/2)color(black)(d=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)color(white)(2/2)|)))
where $\left({x}_{1} , {y}_{1} , {z}_{1}\right) , \left({x}_{2} , {y}_{2} , {z}_{2}\right) \text{ are 2 coordinate points}$

$\text{the 2 points here are " (-6,3,1)" and } \left(2 , - 3 , 1\right)$

$\text{let } \left({x}_{1} , {y}_{1} , {z}_{1}\right) = \left(- 6 , 3 , 1\right) , \left({x}_{2} , {y}_{2} , {z}_{2}\right) = \left(2 , - 3 , 1\right)$

$d = \sqrt{{\left(2 + 6\right)}^{2} + {\left(- 3 - 3\right)}^{2} + {\left(1 - 1\right)}^{2}}$

$\textcolor{w h i t e}{d} = \sqrt{64 + 36 + 0}$

$\textcolor{w h i t e}{d} = \sqrt{100} = 10 \text{ units}$