What is the distance between #(13,-23,-20)# and #(3,-17,-12)#?

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Answer 1 · 2017-05-22T20:17:42

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)(3) - color(blue)(13))^2 + (color(red)(-17) - color(blue)(-23))^2 + (color(red)(-12) - color(blue)(-20))^2)#

#d = sqrt((color(red)(3) - color(blue)(13))^2 + (color(red)(-17) + color(blue)(23))^2 + (color(red)(-12) + color(blue)(20))^2)#

#d = sqrt((-10)^2 + 6^2 + 8^2)#

#d = sqrt(100 + 36 + 64)#

#d = sqrt(200)#

#d = 10sqrt(2)#

#d = 14.142# rounded to the nearest thousandth.