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

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Answer 1 · 2017-02-20T00:01:26

The distance between the two points is #sqrt(33)# or #5.745# 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)(3) - color(blue)(-2))^2 + (color(red)(-1) - color(blue)(1))^2 + (color(red)(1) - color(blue)(3))^2)#

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

#d = sqrt(5^2 + (-2)^2 + (-2)^2)#

#d = sqrt(25 + 4 + 4)#

#d = sqrt(33) = 5.745# rounded to the nearest thousandth.