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Suppose I have a point $(a,b,c)$. What is the distance from this point to the $x$-axis?

I had supposed that it would be simply $\sqrt{b^2+c^2}$ but this does not seem to be the case.

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It is indeed $\sqrt{y^2+z^2}$. What made you think otherwise? – Karolis Juodelė Aug 29 '12 at 13:29
The answer system marks me wrong when I claim this. – Xuan Huang Aug 29 '12 at 13:30
Are you sure you didn't make a mistake elsewhere? The intuition behind this statement is that since $x$ coordinate does not affect the distance to $x$-axis, you can squash the whole space into the $x = 0$ plane and you already know how to find the distance there. – Karolis Juodelė Aug 29 '12 at 13:38
I had the very same intuition- turns out I added the $y^2$ and $z^2$ in question incorrectly. – Xuan Huang Aug 29 '12 at 13:45

In fact is $\sqrt{b^2+c^2}$. You can see this if you think about the point $(a,b,c)$ in the plane $(a,0,0)$.

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