Expert Answer to "Distance between (3,5,-2) and (-8,5,4)?"

wstecznyg5

Answered question

2022-07-14

Distance between (3,5,-2) and (-8,5,4)?

agyalapi60

Beginner2022-07-15Added 17 answers

Recall the very useful formula to calculate the distance in 2 dimensions i.e: between 2 points:

(x_{1}, y_{1}), (x_{2}, y_{2})

d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}

In 3 dimensional space the distance between 3 points is calculated by adding 3rd dimension to the above formula, so now the distance between points:

(x_{1}, y_{1}, z_{1}), (x_{2}, y_{2}, z_{2})

is:

d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2} + {(z_{2} - z_{1})}^{2}}

In this case the points are: (3,5,−2),(−8,5,4) so we have:

d = \sqrt{{(- 11)}^{2} + {(0)}^{2} + {(6)}^{2}}

d = \sqrt{121 + 0 + 36}

d = \sqrt{157}

d \approx 12.53

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