phepafalowl

2022-07-16

Distance between (-2,1,-3) and (5,6,-2)?

yermarvg

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:
$d=\sqrt{{\left(5+2\right)}^{2}+{\left(6-1\right)}^{2}+{\left(-2+3\right)}^{2}}$
$d=\sqrt{{7}^{2}+{5}^{2}+{1}^{2}}$
$d=\sqrt{49+25+1}$
$d=\sqrt{75}$
$d=\sqrt{25\cdot 3}$
$d=5\sqrt{3}$
d=8.660 rounded to the nearest thousandth.

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