What is the distance between #(9,-7,1)# and #(3,-5,-2)#?

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Answer 1 · 2017-02-14T14:51:18

The distance is #sqrt(49)# or #7#

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)(3) - color(blue)(9))^2 + (color(red)(-5) - color(blue)(-7))^2 + (color(red)(-2) - color(blue)(1))^2)#

#d = sqrt((color(red)(3) - color(blue)(9))^2 + (color(red)(-5) + color(blue)(7))^2 + (color(red)(-2) - color(blue)(1))^2)#

#d = sqrt((-6)^2 + 2^2 + (-3)^2)#

#d = sqrt((36 + 4 + 9)#

#d = sqrt(49) = 7#