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

Feb 13, 2016

$\sqrt{35}$

#### Explanation:

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

$d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2} + {\left({z}_{2} - {z}_{1}\right)}^{2}}$

let (x_1 , y_1 , z_1 ) = (-2 ,1 , 3)color(black)(" and (x_2 , y_2 , z_2) = (-1 ,4 , -2 )

substitute these values into the formula.

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

$d = \sqrt{{1}^{2} + {3}^{2} + {\left(- 5\right)}^{2}} = \sqrt{1 + 9 + 25} = \sqrt{35}$