What is the distance between #(13,23,-10)# and #(-3,17,-22)#?

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Answer 1 · 2017-04-11T17:04:54

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)(-3) - color(blue)(13))^2 + (color(red)(17) - color(blue)(23))^2 + (color(red)(-22) - color(blue)(-10))^2)#

#d = sqrt((color(red)(-3) - color(blue)(13))^2 + (color(red)(17) - color(blue)(23))^2 + (color(red)(-22) + color(blue)(10))^2)#

#d = sqrt((-16)^2 + (-6)^2 + (-12)^2)#

#d = sqrt(256 + 36 + 144)#

#d = sqrt(436) = 20.881# rounded to the nearest thousandth.