# What is the distance between A(1,1,1) and B(4,1,-3)?

Apr 16, 2018

$D = 5$ Length Unit

#### Explanation:

The distance between two points in 3_D cartesian Coordinate System can be given by

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

assume that $\left({x}_{1} , {y}_{1} , {z}_{1}\right) = \left(1 , 1 , 1\right)$

then $\left({x}_{2} , {y}_{2} , {z}_{2}\right) = \left(4 , 1 , - 3\right)$

Now Substitute,

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

$D = 5$ Length Unit