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

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

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Answer 1 · 2018-03-13T22:13:58

See a solution process below:

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:

$d = \sqrt{{(- 1 - 8)}^{2} + {(- 3 - - 4)}^{2} + {(5 - 6)}^{2}}$ $d = sqrt((color(red)(-1) - color(blue)(8))^2 + (color(red)(-3) - color(blue)(-4))^2 + (color(red)(5) - color(blue)(6))^2)$

$d = \sqrt{{(- 1 - 8)}^{2} + {(- 3 + 4)}^{2} + {(5 - 6)}^{2}}$ $d = sqrt((color(red)(-1) - color(blue)(8))^2 + (color(red)(-3) + color(blue)(4))^2 + (color(red)(5) - color(blue)(6))^2)$

$d = \sqrt{- 9^{2} + 1^{2} + {(- 1)}^{2}}$ $d = sqrt(-9^2 + 1^2 + (-1)^2)$

$d = \sqrt{81 + 1 + 1}$ $d = sqrt(81+ 1 + 1)$

$d = \sqrt{83}$ $d = sqrt(83)$

Or

$d = 9.110$ $d = 9.110$ rounded to the nearest thousandth.

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

1 Answer

Explanation:

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

1 Answer

Explanation:

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