What is the distance between #(3,-4,15)# and #(12,-11,6)#?

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Answer 1 · 2018-03-11T17:25:52

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)(12) - color(blue)(3))^2 + (color(red)(-11) - color(blue)(-4))^2 + (color(red)(6) - color(blue)(15))^2)#

#d = sqrt((color(red)(12) - color(blue)(3))^2 + (color(red)(-11) + color(blue)(4))^2 + (color(red)(6) - color(blue)(15))^2)#

#d = sqrt(9^2 + (-7)^2 + (-9)^2)#

#d = sqrt(81 + 49 + 81)#

#d = sqrt(211)#

Or

#d = 14.526# rounded to the nearest thousandth.