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Math Help - Finding a point a certain distance from a line.

  1. #1
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    Finding a point a certain distance from a line.


    (I just want to note that I made up this problem. I'm not trying to cheat on a test or anything.)
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  2. #2
    Senior Member Peritus's Avatar
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    \sqrt {(x - 1)^2  + (y - 1)^2 }  = 2
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  3. #3
    MHF Contributor
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    The point satisfies \sqrt{(x-2)^2 + (y-1)^2} = 2 and y = 2x - 3.

    Substitution yields:
    \sqrt{(x-2)^2 + (2x - 4)^2} = 2

    \sqrt{(x-2)^2 + 4(x-2)^2} = 2

    5(x-2)^2 = 4

    (x-2)^2 = \frac{4}{5}

    x-2 = \sqrt{\frac{4}{5}}

    x = \sqrt{\frac{4}{5}} + 2

    Now you plug x back into the line equation to find y.
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  4. #4
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    Clarity

    I just want to clarify that what I'm looking for is the point where that circle is intersecting the line. I'm not looking to solve for the X coordinate.

    So I'm not looking for that answer that's around (4,5) I'm looking for the one that's around (2.9, 2.8)ish – I thought I would need pi.

    If this is in fact the correct solution then I guess I need a little help figuring out what the 1's and 2's represent.
    Last edited by BenBart; October 14th 2008 at 05:39 PM.
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  5. #5
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    How to solve.

    Problems get bumped fairly quickly in this section. Is there a more appropriate place to post this? Geometry, pre-calc?
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