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

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Answer 1 · 2017-02-16T13:31:35

The distance between these two points is $sqrt(38)$ or $6.164$ rounded to the nearest thousandth

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:

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

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

$d = sqrt(2^2 + 3^2 + (-5)^2)$

$d = sqrt(4 + 9 + 25)$

$d = sqrt(38) = 6.164$ rounded to the nearest thousandth

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