What is the distance between #(10,5,-2)# and #(12,11,5)#?

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Answer 1 · 2017-04-29T20:15:35

See the 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)(10))^2 + (color(red)(11) - color(blue)(5))^2 + (color(red)(5) - color(blue)(-2))^2)#

#d = sqrt((color(red)(12) - color(blue)(10))^2 + (color(red)(11) - color(blue)(5))^2 + (color(red)(5) + color(blue)(2))^2)#

#d = sqrt(2^2 + 6^2 + 7^2)#

#d = sqrt(4 + 36 + 49)#

#d = sqrt(89) = 9.434# rounded to the nearest thousandth.