What is the distance between #(-2,1,14)# and #(-12,2,-5)#?

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Answer 1 · 2017-05-22T13:29:52

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)(-12) - color(blue)(-2))^2 + (color(red)(2) - color(blue)(1))^2 + (color(red)(-5) - color(blue)(14))^2)#

#d = sqrt((color(red)(-12) + color(blue)(2))^2 + (color(red)(2) - color(blue)(1))^2 + (color(red)(-5) - color(blue)(14))^2)#

#d = sqrt((-10)^2 + 1^2 + (-19)^2)#

#d = sqrt(100 + 1 + 361)#

#d = sqrt(462)#

#d = 21.494# rounded to the nearest thousandth.