What is the distance between #(–10, –2, 2)# and #(4, –4, –2)#?

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Answer 1 · 2017-04-08T02:15:17

See the entire 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)(4) - color(blue)(-10))^2 + (color(red)(-4) - color(blue)(-2))^2 + (color(red)(-2) - color(blue)(2))^2)#

#d = sqrt((color(red)(4) + color(blue)(10))^2 + (color(red)(-4) + color(blue)(2))^2 + (color(red)(-2) - color(blue)(2))^2)#

#d = sqrt(14^2 + (-2)^2 + (-4)^2)#

#d = sqrt(196 + 4 + 16)#

#d = sqrt(216) = 14.697# rounded to the nearest thousandth.