What is the distance between $(5, –6, 4)$ and $(–5, –1, 1)$ ?

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Answer 1 · 2017-01-16T03:11:00

$d = sqrt(134)$

Or

$d = 11.6$ rounded to the nearest tenth.

The formula for calculating the distance between two points is:

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

Substituting the two points from the problem and solving gives:

$d = sqrt((color(red)(-5) - color(blue)(5))^2 + (color(red)(-1) - color(blue)(-6))^2 + (color(green)(1) - color(green)(4))^2)$

$d = sqrt((-10)^2 + (5)^2 + (-3)^2)$

$d = sqrt(100 + 25 + 9)$

$d = sqrt(134)$

Or

$d = 11.6$ rounded to the nearest tenth.

What is the distance between (5, –6, 4) (5, –6, 4) and (–5, –1, 1)(–5, –1, 1)?