Markus Petty

2022-07-20

What is the distance between (8,-4,6) and (-1,-3,5)?

encoplemt5

Expert

The formula for calculating the distance between two points is:
$d=\sqrt{{\left({x}_{2}-{x}_{1}\right)}^{2}+{\left({y}_{2}-{y}_{1}\right)}^{2}+{\left({z}_{2}-{z}_{1}\right)}^{2}}$
Substituting the values from the points in the problem gives:
$d=\sqrt{{\left(-1-8\right)}^{2}+{\left(-3--4\right)}^{2}+{\left(5-6\right)}^{2}}$
$d=\sqrt{-{9}^{2}+{1}^{2}+{\left(-1\right)}^{2}}$
$d=\sqrt{83}$
Or
$d=9.110$ rounded to the nearest thousandth.

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