What is the distance between #(7,3,-6)# and #(-8,1,-1)#?

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Answer 1 · 2017-02-01T12:40:28

The distance is #sqrt(254)# or #15.94# 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 gives:

#d = sqrt((color(red)(-8) - color(blue)(7))^2 + (color(red)(1) - color(blue)(3))^2 + (color(green)(-1) - color(green)(-6))^2)#

#d = sqrt((color(red)(-8) - color(blue)(7))^2 + (color(red)(1) - color(blue)(3))^2 + (color(green)(-1) + color(green)(6))^2)#

#d = sqrt((-15)^2 + (-2)^2 + (5)^2)#

#d = sqrt(225 + 4 + 25)#

#d = sqrt(254) = 15.94# rounded to the nearest hundredth