What is the distance between #(1,-3,2)# and #(5,4,-3)#?

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Answer 1 · 2017-02-22T16:06:24

The distance between the two points is #sqrt(90)# or #9.487# 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)(5) - color(blue)(1))^2 + (color(red)(4) - color(blue)(-3))^2 + (color(red)(-3) - color(blue)(2))^2)#

#d = sqrt((color(red)(5) - color(blue)(1))^2 + (color(red)(4) + color(blue)(3))^2 + (color(red)(-3) - color(blue)(2))^2)#

#d = sqrt(4^2 + 7^2 + (-5)^2)#

#d = sqrt(16 + 49 + 25)#

#d = sqrt(90) = 9.487#