# What is the distance between (9, 2, 0) and (0, 6, 0) ?

Aug 29, 2016

sqrt97≈9.849

#### Explanation:

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

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2} + {\left({z}_{2} - {z}_{1}\right)}^{2}}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where $\left({x}_{1} , {y}_{1} , {z}_{1}\right) \text{ and " (x_2,y_2,z_2)" are 2 coordinate points}$

here the 2 points are (9 ,2 ,0) and (0 ,6 ,0)

let $\left({x}_{1} , {y}_{1} , {z}_{1}\right) = \left(9 , 2 , 0\right) \text{ and } \left({x}_{2} , {y}_{2} , {z}_{2}\right) = \left(0 , 6 , 0\right)$

d=sqrt((0-9)^2+(6-2)^2+0^2)=sqrt(81+16)=sqrt97≈9.849

Aug 29, 2016

$\sqrt{97}$

#### Explanation:

The (Euclidean) distance between $\left({x}_{1} , {y}_{1} , {z}_{1}\right)$ and $\left({x}_{2} , {y}_{2} , {z}_{2}\right)$ is given by the distance formula:

d = sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2

In our example, $\left({x}_{1} , {y}_{1} , {z}_{1}\right) = \left(9 , 2 , 0\right)$, $\left({x}_{2} , {y}_{2} , {z}_{2}\right) = \left(0 , 6 , 0\right)$ and we find:

$d = \sqrt{{\left(0 - 9\right)}^{2} + {\left(6 - 2\right)}^{2} + {\left(0 - 0\right)}^{2}} = \sqrt{81 + 16 + 0} = \sqrt{97}$