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Wikipedia:Reference desk/Archives/Mathematics/2016 September 2

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September 2

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an oblique kind of distance formula

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Given the angle between two lines, and the signed distance of a point (in the same plane) from each of those lines, what is the point's distance² from their intersection? I've derived this (with difficulty) twice and mislaid my answer; I think it's

but have failed to confirm it, and can't recall how I derived it ... Maybe you know a straightforward derivation? —Tamfang (talk) 09:12, 2 September 2016 (UTC)[reply]

It's easy to see this formula is incorrect, it should reduce to for , infinity for and indeterminate for .
Wlog assume that the intersection is at the origin and that the first line is horizontal. The normalized equation for the second line is . Then letting the point be at , we have and , giving so . -- Meni Rosenfeld (talk) 10:34, 2 September 2016 (UTC)[reply]
I agree it's easy to see that I had it wrong; now that I'm awake I hoped to get here in time to remove it ;)
Resolved
Thanks! —Tamfang (talk) 17:03, 2 September 2016 (UTC)[reply]