What is the distance between #(2,-4,6)# and #(-9,-5,9)#?

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Answer 1 · 2018-06-14T19:51:21

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)(-9) - color(blue)(2))^2 + (color(red)(-5) - color(blue)(-4))^2 + (color(red)(9) - color(blue)(6))^2)#

#d = sqrt((color(red)(-9) - color(blue)(2))^2 + (color(red)(-5) + color(blue)(4))^2 + (color(red)(9) - color(blue)(6))^2)#

#d = sqrt((-11)^2 + (-1)^2 + (3)^2)#

#d = sqrt(121 + 1 + 9)#

#d = sqrt(131)#

Or, approximately:

#d ~= 11.4455#