# What is the distance between (3,-12,12) and (-1,13,-12)?

Sep 19, 2016

The distance betwen $\left(3 , - 12 , 12\right)$ and $\left(- 1 , 13 , - 12\right)$ is $34.886$

#### Explanation:

In a three dimensional space, the distance between two points $\left({x}_{1} , {y}_{1} , {z}_{1}\right)$ and $\left({x}_{2} , {y}_{2} , {z}_{2}\right)$ is given by

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

Hence, the distance betwen $\left(3 , - 12 , 12\right)$ and $\left(- 1 , 13 , - 12\right)$ is

$\sqrt{{\left(\left(- 1\right) - 3\right)}^{2} + {\left(13 - \left(- 12\right)\right)}^{2} + {\left(\left(- 12\right) - 12\right)}^{2}}$

= $\sqrt{{\left(- 4\right)}^{2} + {\left(25\right)}^{2} + {\left(- 24\right)}^{2}}$

= $\sqrt{16 + 625 + 576}$

= $\sqrt{1217}$

= $34.886$