What is the distance between #(5, –6, 4) # and #(–5, –1, 1)#?

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Answer 1 · 2017-01-16T03:11:00

#d = sqrt(134)#

Or

#d = 11.6# rounded to the nearest tenth.

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(green)(z_2) - color(green)(z_1))^2)#

Substituting the two points from the problem and solving gives:

#d = sqrt((color(red)(-5) - color(blue)(5))^2 + (color(red)(-1) - color(blue)(-6))^2 + (color(green)(1) - color(green)(4))^2)#

#d = sqrt((-10)^2 + (5)^2 + (-3)^2)#

#d = sqrt(100 + 25 + 9)#

#d = sqrt(134)#

Or

#d = 11.6# rounded to the nearest tenth.