Markus Petty

2022-07-17

What is the distance between (4,2,6) and (7,3,6)?

lelapem

Expert

The distance, (D) between two points in 3-space $\left({x}_{1},{y}_{1},{z}_{1}\right)\phantom{\rule{1ex}{0ex}}\text{and}\phantom{\rule{1ex}{0ex}}\left({x}_{2},{y}_{2},{z}_{2}\right)$ is given by:
$D=\sqrt{{\left({x}_{1}-{x}_{2}\right)}^{2}+{\left({y}_{1}-{y}_{2}\right)}^{2}+{\left({z}_{1}-{z}_{2}\right)}^{2}}$
In this example: ${x}_{1}=4,{y}_{1}=2,{z}_{1}=6\phantom{\rule{1ex}{0ex}}\text{and}\phantom{\rule{1ex}{0ex}}{x}_{2}=7,{y}_{2}=3,{z}_{2}=6$
Hence $D=\sqrt{{\left(4-7\right)}^{2}+{\left(2-3\right)}^{2}+{\left(6-6\right)}^{2}}$
$=\sqrt{{\left(-3\right)}^{2}+{\left(-1\right)}^{2}+{\left(0\right)}^{2}}$
$=\sqrt{10}$ units

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