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

May 6, 2016

$1$

#### Explanation:

The distance between $\left({x}_{1} , {y}_{1} , {z}_{1}\right) = \left(0 , 4 , - 2\right)$ and $\left({x}_{2} , {y}_{2} , {z}_{2}\right) = \left(- 1 , 4 , - 2\right)$ is given by the distance formula:

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

sqrt((-1-0)^2+(4-4)^2+(-2-(-2))^2))

$= \sqrt{1 + 0 + 0}$

$= \sqrt{1} = 1$

Alternatively, simply notice that the $y$ and $z$ coordinates of the two points is identical, so the points only differ in the $x$ coordinate and the distance between the points is just the absolute change in the $x$ coordinate, namely $1$.