What is the distance between #(3,-29,-12)# and #(2,-38,-6)#?

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Answer 1 · 2018-03-07T08:49:12

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)(2) - color(blue)(3))^2 + (color(red)(-38) - color(blue)(-29))^2 + (color(red)(-6) - color(blue)(-12))^2)#

#d = sqrt((color(red)(2) - color(blue)(3))^2 + (color(red)(-38) + color(blue)(29))^2 + (color(red)(-6) + color(blue)(12))^2)#

#d = sqrt((-1)^2 + (-9)^2 + 6^2)#

#d = sqrt(1 + 81 + 36)#

#d = sqrt(118)#

Or if a non-radical answer is required:

#d = 10.863# rounded to the nearest thousandth.