What is the distance between # (–2, 1, 3) # and #(0, 4, –2) #?

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Answer 1 · 2018-03-03T16:23:38

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)(0) - color(blue)(-2))^2 + (color(red)(4) - color(blue)(1))^2 + (color(red)(-2) - color(blue)(3))^2)#

#d = sqrt((color(red)(0) + color(blue)(2))^2 + (color(red)(4) - color(blue)(1))^2 + (color(red)(-2) - color(blue)(3))^2)#

#d = sqrt(2^2 + 3^2 + (-5)^2)#

#d = sqrt(4 + 9 + 25)#

#d = sqrt(38)#

Or

#d = 6.164# rounded to the nearest thousandth.