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

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Answer 1 · 2018-03-07T11:45:32

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:

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

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

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

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

$d = sqrt(43)$

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