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

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Answer 1 · 2017-05-08T22:04:17

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

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

#d = sqrt(3^2 + 4^2 + (-4)^2)#

#d = sqrt(9 + 16 + 16)#

#d = sqrt(41) = 6.403# rounded to the nearest thousandth