What is the distance between #(-7,-6,4)# and #(-2,3,4)#?

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Answer 1 · 2017-09-29T12:21:13

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)(-2) - color(blue)(-7))^2 + (color(red)(3) - color(blue)(-6))^2 + (color(red)(4) - color(blue)(4))^2)#

#d = sqrt((color(red)(-2) + color(blue)(7))^2 + (color(red)(3) + color(blue)(6))^2 + (color(red)(4) - color(blue)(4))^2)#

#d = sqrt(5^2 + 9^2 + 0^2)#

#d = sqrt(25 + 81 + 0)#

#d = sqrt(106)#

Or, if you need a single number:

#d = 10.296# rounded to the nearest thousandth