# What is the distance between (–3, 2, –3)  and (0, 4, –2) ?

Apr 21, 2018

color(violet)("Distance " d = sqrt 14 ~~ 3.74 " units"

#### Explanation:

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

$\text{Given : } \left({x}_{1} , {y}_{1} , {z}_{1}\right) = \left(- 3 , 2 , - 3\right) , \left({x}_{2} , {y}_{2} , {z}_{2}\right) = \left(0 , 4 , - 2\right)$

$d = \sqrt{{\left(0 + 3\right)}^{2} + {\left(4 - 2\right)}^{2} + {\left(- 2 + 3\right)}^{2}} = \sqrt{9 + 4 + 1}$

color(violet)("Distance " d = sqrt 14 ~~ 3.74 " units"