What is the distance between #(3,-2,-12)# and #(5,-8,-16)#?

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Answer 1 · 2017-02-08T21:10:02

The distance between the points is #sqrt(56)# or #7.48# rounded to the nearest hundredth.

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 and calculating gives:

#d = sqrt((color(red)(5) - color(blue)(3))^2 + (color(red)(-8) - color(blue)(-2))^2 + (color(red)(-16) - color(blue)(-12))^2)#

#d = sqrt((color(red)(5) - color(blue)(3))^2 + (color(red)(-8) + color(blue)(2))^2 + (color(red)(-16) + color(blue)(12))^2)#

#d = sqrt(2^2 + (-6)^2 + (-4)^2)#

#d = sqrt(4 + 36 + 16)#

#d = sqrt(56) = 7.48# rounded to the nearest hundredth.