What is the distance between $(–6, 3, 4)$ and $(4, –4, –2)$ ?

Question

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Answer 1 · 2018-03-10T02:56:07

See a solution process below:

The formula for calculating the distance between two points is:

$d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2 + (color(red)(z_2) - color(blue)(z_1))^2)$

Substituting the values from the points in the problem gives:

$d = sqrt((color(red)(4) - color(blue)(-6))^2 + (color(red)(-4) - color(blue)(3))^2 + (color(red)(-2) - color(blue)(4))^2)$

$d = sqrt((color(red)(4) + color(blue)(6))^2 + (color(red)(-4) - color(blue)(3))^2 + (color(red)(-2) - color(blue)(4))^2)$

$d = sqrt(10^2 + (-7)^2 + (-6)^2)$

$d = sqrt(100 + 49 + 36)$

$d = sqrt(185)$

Or

$d = 13.601$ rounded to the nearest thousandth

What is the distance between (–6, 3, 4) (–6, 3, 4) and (4, –4, –2)(4, –4, –2)?