What is the distance between #(0, 0, 8) # and #(6, 8, 2) #?

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Answer 1 · 2017-01-21T19:28:50

The distance between the points is #sqrt(136)# or #11.66# rounded to the nearest hundredth

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 values from the points in the problem and calculating for #d# gives:

#d = sqrt((color(red)(6) - color(blue)(0))^2 + (color(red)(8) - color(blue)(0))^2 + (color(green)(2) - color(green)(8))^2)#

#d = sqrt((6)^2 + (8)^2 + (-6)^2)#

#d = sqrt(36 + 64 + 36)#

#d = sqrt(136) = 11.66# rounded to the nearest hundredth