Lilliana Livingston

2022-07-23

Distance between (3,-2,-2) and (5,-4,-6)?

jbacapzh

Expert

The distance between the two points can be found using a kind of extended Pythagoras formula:
${d}_{{1}_{2}}=\sqrt{{\left({x}_{2}-{x}_{1}\right)}^{2}+{\left({y}_{2}-{y}_{1}\right)}^{2}+{\left({z}_{2}-{z}_{1}\right)}^{2}}$
so, using our coordinates given in the problem:
$d=\sqrt{{\left(5-3\right)}^{2}+{\left[-4-\left(-2\right)\right]}^{2}+{\left[-6-\left(-2\right)\right)}^{2}}=\sqrt{4+4+16}=\sqrt{24}=4.89\text{units}$
$d=\sqrt{{\left(5-3\right)}^{2}+{\left[-4-\left(-2\right)\right]}^{2}+{\left[-6-\left(-2\right)\right)}^{2}}=\sqrt{4+4+16}=\sqrt{24}=4.89\text{units}$

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