What is the distance between #(–1, 1, 3) # and #(4, –1, 2)#?

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Answer 1 · 2017-01-24T17:17:12

The distance is #sqrt(30)# or #5.48# 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(green)(z_2) - color(green)(z_1))^2)#

Substituting the values from the problem gives:

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

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

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

#d = sqrt(25 + 4 + 1)#

#d = sqrt(30) = 5.48# rounded to the nearest hundredth