What is the distance between $(2, 1, - 7)$ $(2,1,-7)$ and $(1, 5, 3)$ $(1,5,3)$ ?

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What is the distance between $(2, 1, - 7)$ $(2,1,-7)$ and $(1, 5, 3)$ $(1,5,3)$ ?

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Answer 1 · 2017-04-08T01:56:55

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Explanation:

The formula for calculating the distance between two points is:

$d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2} + {(z_{2} - z_{1})}^{2}}$ $d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2 + (color(red)(z_2) - color(blue)(z_1))^2)$

Substituting the values from the points in the problem gives:

$d = \sqrt{{(1 - 2)}^{2} + {(5 - 1)}^{2} + {(3 - - 7)}^{2}}$ $d = sqrt((color(red)(1) - color(blue)(2))^2 + (color(red)(5) - color(blue)(1))^2 + (color(red)(3) - color(blue)(-7))^2)$

$d = \sqrt{{(1 - 2)}^{2} + {(5 - 1)}^{2} + {(3 + 7)}^{2}}$ $d = sqrt((color(red)(1) - color(blue)(2))^2 + (color(red)(5) - color(blue)(1))^2 + (color(red)(3) + color(blue)(7))^2)$

$d = \sqrt{{(- 1)}^{2} + 4^{2} + 10^{2}}$ $d = sqrt((-1)^2 + 4^2 + 10^2)$

$d = \sqrt{1 + 16 + 100}$ $d = sqrt(1 + 16 + 100)$

$d = \sqrt{117} = 10.817$ $d = sqrt(117) = 10.817$ rounded to the nearest thousandth.

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What is the distance between $(2, 1, - 7)$ $(2,1,-7)$ and $(1, 5, 3)$ $(1,5,3)$ ?

1 Answer

Explanation:

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