# What is the distance of the (2, 3, 5) and (2, 7, 4)?

Apr 10, 2016

$\sqrt{17}$

#### Explanation:

To calculate the distance between the 2 points use the 3-d version of the $\textcolor{b l u e}{\text{ distance formula }}$

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2} + {\left({z}_{2} - {z}_{1}\right)}^{2}}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

where $\left({x}_{1} , {y}_{1} , {z}_{1}\right) \text{ and " (x_2,y_2,z_2)" are 2 coord points }$

let $\left({x}_{1} , {y}_{1} , {z}_{1}\right) = \left(2 , 3 , 5\right) \text{ and } \left({x}_{2} , {y}_{2} , {z}_{2}\right) = \left(2 , 7 , 4\right)$

rArr d = sqrt((2-2)^2+(7-3)^2+(4-5)^2

$= \sqrt{0 + 16 + 1} = \sqrt{17}$