# Distance between (-5,13,-14) and (-11,4,1)?

Distance between (-5,13,-14) and (-11,4,1)?
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Messiah Trevino
Treat the way you would a triangle using Pythagoras but with 3 values instead of two.
Let the length between the two points be L
Let point 1 $\to {P}_{1}\to \left({x}_{1},{y}_{1},{z}_{1}\right)\to \left(-5,13,-14\right)$
Let point 2 $\to {P}_{2}\to \left({x}_{2},{y}_{2},{z}_{2}\right)\to \left(-11,4,1\right)$
Then
${L}^{2}={\left({x}_{2}-{x}_{1}\right)}^{2}+{\left({y}_{2}-{y}_{1}\right)}^{2}+{\left({z}_{2}-{z}_{1}\right)}^{2}$
So $L=\sqrt{{\left(-11-\left[-5\right]\right)}^{2}+{\left(4-13\right)}^{2}+{\left(1-\left[-14\right]\right)}^{2}}$
$L=\sqrt{36+81+225}=\sqrt{342}$
But $342=2×{3}^{2}×19$ but both 19 and 2 are prime numbers
$⇒L=3\sqrt{38}$