What is the distance between #(-13,13,-4)# and #(-1,-6,-2)#?

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Answer 1 · 2018-03-09T14:30:42

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)(-1) - color(blue)(-13))^2 + (color(red)(-6) - color(blue)(13))^2 + (color(red)(-2) - color(blue)(-4))^2)#

#d = sqrt((color(red)(-1) + color(blue)(13))^2 + (color(red)(-6) - color(blue)(13))^2 + (color(red)(-2) + color(blue)(4))^2)#

#d = sqrt(12^2 + (-19)^2 + 2^2)#

#d = sqrt(144 + 361 + 4)#

#d = sqrt(509)#

Or

#d = 22.561# rounded to the nearest thousandth