What is the distance between #(–2, 2, 6) # and #(–5, –1, 1) #?

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Answer 1 · 2018-03-07T11:45:32

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

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

#d = sqrt((-3)^2 + (-3)^2 + (-5)^2)#

#d = sqrt(9 + 9 + 25)#

#d = sqrt(43)#