What is the distance between $(-2,1,-3)$ and $(5,6,-2)$ ?

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Answer 1 · 2018-01-09T13:26:01

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:

$d = sqrt((color(red)(5) - color(blue)(-2))^2 + (color(red)(6) - color(blue)(1))^2 + (color(red)(-2) - color(blue)(-3))^2)$

$d = sqrt((color(red)(5) + color(blue)(2))^2 + (color(red)(6) - color(blue)(1))^2 + (color(red)(-2) + color(blue)(3))^2)$

$d = sqrt(7^2 + 5^2 + 1^2)$

$d = sqrt(49 + 25 + 1)$

$d = sqrt(75)$

$d = sqrt(25 * 3)$

$d = sqrt(25)sqrt(3)$

$d = 5sqrt(3)$

Or

$d = 8.660$ rounded to the nearest thousandth.

What is the distance between (-2,1,-3)(-2,1,-3) and (5,6,-2)(5,6,-2)?