# What is the distance between (6, 8, 2)  and (8, 6, 2) ?

Apr 13, 2016

$2 \sqrt{2}$

#### Explanation:

color(blue)((6,8,2) and (8,6,2)

Use the $\text{3-dimensional}$ Distance formula

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

Where

color(indigo)(d="distance"

So,

color(indigo)(underbrace("(6,8,2) and (8,6,2)")_((x_1,y_1,z_1) and (x_2,y_2,z_2))

color(violet)(x_1=6,x_2=8

color(violet)(y_1=8,y_2=6

color(violet)(z_1=2,z_2=2

$\rightarrow d = \sqrt{{\left(8 - 6\right)}^{2} + {\left(8 - 6\right)}^{2} + {\left(2 - 2\right)}^{2}}$

$\rightarrow d = \sqrt{{\left(2\right)}^{2} + {\left(2\right)}^{2} + {\left(0\right)}^{2}}$

$\rightarrow d = \sqrt{4 + 4 + 0}$

color(green)(rArrd=sqrt(8)=sqrt(4*2)=2sqrt2