# What is the distance between (8,-7,-4) and (9,2,2)?

Feb 24, 2016

$D = \sqrt{118} \cong 10.86$

#### Explanation:

Note: The distance formula in 3D is

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

We are given ordered triplet in $x , y , z$ , as follow

$\left(8 , - 7 , - 4\right) \text{ and } \left(9 , 2 , 2\right)$

$D = \sqrt{{\left(8 - 9\right)}^{2} + {\left(- 7 - 2\right)}^{2} + {\left(- 4 - 2\right)}^{2}}$

$D = \sqrt{{\left(- 1\right)}^{2} + {\left(- 9\right)}^{2} + {\left(- 6\right)}^{2}}$

$D = \sqrt{\left(1\right) + \left(81\right) + \left(36\right)}$

$D = \sqrt{118} \cong 10.86$