What is the distance between $(-1,-1,-1)$ and $(1,1,1)$ ?

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Answer 1 · 2018-03-26T01:23:34

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:

$d = sqrt((color(red)(1) - color(blue)(-1))^2 + (color(red)(1) - color(blue)(-1))^2 + (color(red)(1) - color(blue)(-1))^2)$

$d = sqrt((color(red)(1) + color(blue)(1))^2 + (color(red)(1) + color(blue)(1))^2 + (color(red)(1) + color(blue)(1))^2)$

$d = sqrt(2^2 + 2^2 + 2^2)$

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

$d = sqrt(12)$

$d = sqrt(4 * 3)$

$d = sqrt(4)sqrt(3)$

$d = 2sqrt(3)$

Or

$d ~= 3.464$

What is the distance between (-1,-1,-1)(-1,-1,-1) and (1,1,1)(1,1,1)?