# What is the distance between (5, –6, 4)  and (–6, 3, 4)?

Dec 6, 2015

$\sqrt{202}$

#### Explanation:

The distance between two points (in any dimension greater than or equal to $2$), is given by the square root of the sum of the squares of the differences of the correspondant coordinates. It's easier to write it in formulas than in words: if the two points are $\left({x}_{1} , {y}_{1} , {z}_{1}\right)$ and $\left({x}_{2} , {y}_{2} , {z}_{2}\right)$, then the distance is

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

sqrt( (5+6)^2 + (-6-3)^2 + (4-4)^2 ) =sqrt(11^2+(--)^2)
$= \sqrt{121 + 81} = \sqrt{202}$