What is the distance between $(–2, 1, 3)$ and $(–4, 3, 0)$ ?

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Answer 1 · 2018-06-01T19:16:59

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:

$d = sqrt((color(red)(-4) - color(blue)(-2))^2 + (color(red)(3) - color(blue)(1))^2 + (color(red)(0) - color(blue)(3))^2)$

$d = sqrt((color(red)(-4) + color(blue)(2))^2 + (color(red)(3) - color(blue)(1))^2 + (color(red)(0) - color(blue)(3))^2)$

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

$d = sqrt(4 + 4 + 9)$

$d = sqrt(17)$

Or, approximately

$d = 4.123$

What is the distance between (–2, 1, 3) (–2, 1, 3) and (–4, 3, 0) (–4, 3, 0) ?