What is the distance between $(2,-4,6)$ and $(-9,-5,9)$ ?

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Answer 1 · 2018-06-14T19:51:21

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:

$d = sqrt((color(red)(-9) - color(blue)(2))^2 + (color(red)(-5) - color(blue)(-4))^2 + (color(red)(9) - color(blue)(6))^2)$

$d = sqrt((color(red)(-9) - color(blue)(2))^2 + (color(red)(-5) + color(blue)(4))^2 + (color(red)(9) - color(blue)(6))^2)$

$d = sqrt((-11)^2 + (-1)^2 + (3)^2)$

$d = sqrt(121 + 1 + 9)$

$d = sqrt(131)$

Or, approximately:

$d ~= 11.4455$

What is the distance between (2,-4,6)(2,-4,6) and (-9,-5,9)(-9,-5,9)?