What is the distance between #(5, –6, 4) # and #(–10, –2, 2)#?

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Answer 1 · 2017-03-30T02:46:16

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)(-10) - color(blue)(5))^2 + (color(red)(-2) - color(blue)(-6))^2 + (color(red)(2) - color(blue)(4))^2)#

#d = sqrt((color(red)(-10) - color(blue)(5))^2 + (color(red)(-2) + color(blue)(6))^2 + (color(red)(2) - color(blue)(4))^2)#

#d = sqrt((-15)^2 + 4^2 + (-2)^2)#

#d = sqrt(225 + 16 + 4)#

#d = sqrt(245) = 15.652# rounded to the nearest thousandth.