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

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Answer 1 · 2017-02-25T22:45:02

The distance between the two points is #sqrt(86)# or #9.274# rounded to the nearest hundredth

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

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

#d = sqrt((-6)^2 + 7^2 + (-1)^2)#

#d = sqrt(36 + 49 + 1)#

#d = sqrt(86) = 9.274# rounded to the nearest hundredth