# What is the distance between (13,-13,1) and (22,-1,6)?

Mar 6, 2018

$15.81$ units

#### Explanation:

For the distance between two points on a three-dimensional graph, the following formula is used:

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

Here, $\left({x}_{1} , {y}_{2} , {z}_{1}\right) = \left(13 , - 13 , 1\right)$ and $\left({x}_{2} , {y}_{2} , {z}_{2}\right) = \left(22 , - 1 , 6\right)$.

Inputting:

$d = | \sqrt{{\left(22 - 13\right)}^{2} + {\left(- 1 - \left(- 13\right)\right)}^{2} + {\left(6 - 1\right)}^{2}} |$

$d = | \sqrt{{9}^{2} + {12}^{2} + {5}^{2}} |$

$d = | \sqrt{81 + 144 + 25} |$

$d = | \sqrt{250} |$

$d = 15.81$ units