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

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Answer 1 · 2017-04-08T01:56:55

See the entire 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)(1) - color(blue)(2))^2 + (color(red)(5) - color(blue)(1))^2 + (color(red)(3) - color(blue)(-7))^2)#

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

#d = sqrt((-1)^2 + 4^2 + 10^2)#

#d = sqrt(1 + 16 + 100)#

#d = sqrt(117) = 10.817# rounded to the nearest thousandth.