# What is the distance between (-3,9,1) and (2,-5,-6)?

Oct 1, 2017

$\sqrt{270}$

#### Explanation:

The formula for distance in three dimensions is:

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

So, for your example: $\sqrt{{\left(- 6 - 1\right)}^{2} + {\left(- 5 - 9\right)}^{2} + {\left(2 - \left(- 3\right)\right)}^{2}}$

Which is equal to $\sqrt{49 + 196 + 25}$

$= \sqrt{270}$

$\approx 16.43$