What is the distance between $(- 3, 9, 1)$ $(-3,9,1)$ and $(2, - 5, - 6)$ $(2,-5,-6)$ ?

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Answer 1 · 2017-10-01T20:40:42

$\sqrt{270}$ $sqrt 270$

The formula for distance in three dimensions is:

$\sqrt{{(z_{2} - z_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2} + {(x_{2} - x_{1})}_{2}^{2}}$ $sqrt ((z_2 - z_1)^2 + (y_2 - y_1)^2 + (x_2 - x_1)^2)$

So, for your example: $\sqrt{{(- 6 - 1)}^{2} + {(- 5 - 9)}^{2} + {(2 - (- 3))}^{2}}$ $sqrt((-6 -1)^2 + (-5-9)^2 + (2-(-3))^2)$

Which is equal to $\sqrt{49 + 196 + 25}$ $sqrt (49+196+25)$

$= \sqrt{270}$ $= sqrt 270$

$\approx 16.43$ $~~ 16.43$

What is the distance between (−3,9,1)(-3,9,1) and (2,−5,−6)(2,-5,-6)?