What is the distance between #(3, –1, 1) # and #(8, 6, 0) #?

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Answer 1 · 2017-05-05T12:15:33

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)(8) - color(blue)(3))^2 + (color(red)(6) - color(blue)(-1))^2 + (color(red)(0) - color(blue)(1))^2)#

#d = sqrt((color(red)(8) - color(blue)(3))^2 + (color(red)(6) + color(blue)(1))^2 + (color(red)(0) - color(blue)(1))^2)#

#d = sqrt(5^2 + 7^2 + (-1)^2)#

#d = sqrt(25 + 49 + 1)#

#d = sqrt(75) = 8.660# rounded to the nearest thousandth.