What is the distance between $(13,-23,-20)$ and $(-3,-37,-22)$ ?

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Answer 1 · 2018-06-23T13:21:56

See a solution process below:

The formula for calculating the distance between two points is:

$d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2 + (color(red)(z_2) - color(blue)(z_1))^2)$

Where $(color(blue)(x_1), color(blue)(y_1), color(blue)(z_1))$ and $(color(red)(x_1), color(red)(y_1), color(red)(z_1))$ are two points.

Substituting the values from the points in the problem gives:

$d = sqrt((color(red)(-3) - color(blue)(13))^2 + (color(red)(-37) - color(blue)(-23))^2 + (color(red)(-22) - color(blue)(-20))^2)$

$d = sqrt((color(red)(-3) - color(blue)(13))^2 + (color(red)(-37) + color(blue)(23))^2 + (color(red)(-22) + color(blue)(20))^2)$

$d = sqrt((-16)^2 + (-14)^2 + (-2)^2)$

$d = sqrt(256 + 196 + 4)$

$d = sqrt(456)$

$d = sqrt(4 * 114)$

$d = sqrt(4)sqrt(114)$

$d = 2sqrt(114)$

Or, approximately:

$d ~= 21.354$

What is the distance between (13,-23,-20)(13,-23,-20) and (-3,-37,-22)(-3,-37,-22)?