What is the distance between #(2,12,5)# and #(-1,7,5)#?

1 Answer
Feb 25, 2017

Answer:

The distance between the two points is #sqrt(34)# or #5.831# rounded to the nearest thousandth.

Explanation:

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)(-1) - color(blue)(2))^2 + (color(red)(7) - color(blue)(12))^2 + (color(red)(5) - color(blue)(5))^2)#

#d = sqrt((-3)^2 + (-5)^2 + 0^2)#

#d = sqrt(9 + 25 + 0)#

#d = sqrt(34) = 5.831# rounded to the nearest thousandth.