What is the distance between # (–2, 1, 3) # and #(–1, 2, –3) #?

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Answer 1 · 2017-02-12T12:43:28

The distance between the points is #sqrt(11)# or #3.317# rounded to the nearest thousandth.

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)(2) - color(blue)(1))^2 + (color(red)(-3) - color(blue)(3))^2)#

#d = sqrt((color(red)(-1) + color(blue)(2))^2 + (color(red)(2) - color(blue)(1))^2 + (color(red)(-3) - color(blue)(3))^2)#

#d = sqrt(1^2 + 1^2 + (-3)^2)#

#d = sqrt(1 + 1 + 9)#

#d = sqrt(11) = 3.317# rounded to the nearest thousandth.