What is the distance between #(8,-4,6)# and #(-1,-3,5)#?

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Answer 1 · 2018-03-13T22:13:58

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)(-1) - color(blue)(8))^2 + (color(red)(-3) - color(blue)(-4))^2 + (color(red)(5) - color(blue)(6))^2)#

#d = sqrt((color(red)(-1) - color(blue)(8))^2 + (color(red)(-3) + color(blue)(4))^2 + (color(red)(5) - color(blue)(6))^2)#

#d = sqrt(-9^2 + 1^2 + (-1)^2)#

#d = sqrt(81+ 1 + 1)#

#d = sqrt(83)#

Or

#d = 9.110# rounded to the nearest thousandth.