What is the distance between $(2,-14,6)$ and $(-9,5,9)$ ?

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Answer 1 · 2018-04-18T03:48:32

$color(red)(d = sqrt491)$ or $color(red)(~~22.159)$ (rounded to thousandth's place)

The distance between three dimensions is similar to the distance between two dimensions.

We use the formula:
$quadcolor(red)(d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2))$ , where $x$ , $y$ , and $z$ are the coordinates.

Let's plug in the values for the coordinates into the formula. Pay attention to the negative signs:
$quadd = sqrt((-9-2)^2 + (5-(-14))^2 + (9-6)^2)$

And now simplify:
$quadd = sqrt((-11)^2 + (19)^2 + (3)^2)$

$quadd = sqrt(121+361+81)$

$quadcolor(red)(d = sqrt491)$ or $color(red)(~~22.159)$ (rounded to thousandth's place)

Hope this helps!

What is the distance between (2,-14,6)(2,-14,6) and (-9,5,9)(-9,5,9)?