# What is the distance between  (8, 6, 0)  and (–1, 4, –2) ?

Feb 20, 2016

 sqrt89 ≈ 9.43

#### Explanation:

To calculate the distance between these 2 points use the $\textcolor{b l u e}{\text{ 3-dimensional version of the distance formula}}$

 d = sqrt((x_2 - x_1)^2 +(y_2 - y_1)^2 + (z_2 - z_1)^2

where $\left({x}_{1} , {y}_{1} , {z}_{1}\right) \text{ and "(x_2,y_2,z_2) " are the coords of the 2 points}$

here let$\left({x}_{1} , {y}_{1} , {z}_{1}\right) = \left(8 , 6 , 0\right) \text{ and } \left({x}_{2} , {y}_{2} , {z}_{2}\right) = \left(- 1 , 4 , - 2\right)$

$\Rightarrow d = \sqrt{{\left(- 1 - 8\right)}^{2} + {\left(4 - 6\right)}^{2} + {\left(- 2 - 0\right)}^{2}} = \sqrt{81 + 4 + 4} = \sqrt{89}$