# What is the distance between (8, 6, 2)  and (3, 4, 1) ?

Aug 6, 2016

$\sqrt{30}$

#### Explanation:

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

Given 2 coordinate points $\left({x}_{1} , {y}_{1} , {z}_{1}\right) \text{ and } \left({x}_{2} , {y}_{2} , {z}_{2}\right)$

Then the distance between them ( d) is

color(red)(|bar(ul(color(white)(a/a)color(black)(d=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)color(white)(a/a)|)))

let $\left({x}_{1} , {y}_{1} , {z}_{1}\right) = \left(8 , 6 , 2\right) \text{ and } \left({x}_{2} , {y}_{2} , {z}_{2}\right) = \left(3 , 4 , 1\right)$

$d = \sqrt{{\left(3 - 8\right)}^{2} + {\left(4 - 6\right)}^{2} + {\left(1 - 2\right)}^{2}} = \sqrt{25 + 4 + 1} = \sqrt{30}$