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Thread: Line Distance

  1. #1
    Senior Member polymerase's Avatar
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    Line Distance

    A line passes through the points $\displaystyle ({1,\dfrac{1}{8}})$ and intersects the positive x-axis at the point A and the positive y-axis at the point B. What is the shortest possible distance between A and B?
    Last edited by polymerase; Dec 2nd 2007 at 08:40 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by polymerase View Post
    A line passes through the points $\displaystyle ({1,\dfrac{1}{8}})$ and intersects the positive x-axis at the point A and the positive y-axis at the point B. What is the shortest possible distance between A and B?
    Suppose the point $\displaystyle B$ is $\displaystyle (0, b) $, then the line is:

    $\displaystyle
    y=\frac{1/8 - b}{1}x + b
    $

    and this meets the x-axis at $\displaystyle A = (-b/(1/8 - b),0)$

    Now you can find the distance between $\displaystyle A$ and $\displaystyle B$ as a function of b.

    Then find the $\displaystyle b$ which gives the minimum for this distance and the corresponding distance.

    RonL
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  3. #3
    Senior Member polymerase's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    Suppose the point $\displaystyle B$ is $\displaystyle (0, b) $, then the line is:

    $\displaystyle
    y=\frac{1/8 - b}{1}x + b
    $

    and this meets the x-axis at $\displaystyle A = (-b/(1/8 - b),0)$

    Now you can find the distance between $\displaystyle A$ and $\displaystyle B$ as a function of b.

    Then find the $\displaystyle b$ which gives the minimum for this distance and the corresponding distance.

    RonL
    I don't get how you obtain the part where you said that it meets the x-axis at $\displaystyle A = (-b/(1/8 - b),0)$....
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