What is the distance between $(3,-14,15)$ and $(12,-21,16)$ ?

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Answer 1 · 2018-04-27T12:37:39

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:

$d = sqrt((color(red)(12) - color(blue)(3))^2 + (color(red)(-21) - color(blue)(-14))^2 + (color(red)(16) - color(blue)(15))^2)$

$d = sqrt((color(red)(12) - color(blue)(3))^2 + (color(red)(-21) + color(blue)(14))^2 + (color(red)(16) - color(blue)(15))^2)$

$d = sqrt(9^2 + (-7)^2 + 1^2)$

$d = sqrt(81 + 49 + 1)$

$d = sqrt(131)$

Or

$d ~= 11.45$

What is the distance between (3,-14,15)(3,-14,15) and (12,-21,16)(12,-21,16)?