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

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Answer 1 · 2018-03-07T08:10:46

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

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

#d = sqrt((-4)^2 + (-2)^2 + (-2)^2)#

#d = sqrt(16 + 4 + 4)#

#d = sqrt(24)#

#d = sqrt(4 * 6)#

#d = sqrt(4)sqrt(6)#

#d = 2sqrt(6)#

Or, if you require a non-radical answer:

#d = 4.899# rounded to the nearest thousandth