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Homework Help: Getting a rhombus vertex from one vertex and its area

  1. Jun 9, 2010 #1
    Hi there. Im tryin to solve this one, I know that if I find the way to get one more vertex i'd have it solved.

    1. The problem statement, all variables and given/known data
    The point A(-1,8) is the vertex of a rhombus which minor diagonal is situated on the line L: [tex]L=\begin{Bmatrix} x=3\mu & \mbox{ }& \\y=1+4\mu & \mbox{}&\end{matrix}
    [/tex], [tex]\mu\in{R}[/tex]. Get the coordinates of the rest of the vertex knowing that the rhombus area is 30.

    2. Relevant equations
    [tex]A=\displaystyle\frac{dD}{2}[/tex]


    3. The attempt at a solution
    Well, I haven't done too much. Actually I did some, but then I realized that I had confused something, cause I got the line L' where would be located the major D, but I've used for it the point A, and then I was trying to get the point of intersection between L and L', so then I doubled it, and I was going to get my second vertex, but then I realized that it was wrong, cause I couln't use point A, cause A don't belongs to L', it belongs to L, so...

    [tex]30=\displaystyle\frac{dD}{2}\Rightarrow{60=dD}[/tex]

    So, I don't know much about L', but that its perpendicular to L.

    [tex]L'=\begin{Bmatrix} x=x_0+4/3\lambda & \mbox{ }& \\y=y_0-\lambda & \mbox{}&\end{matrix}
    [/tex]
     
    Last edited: Jun 9, 2010
  2. jcsd
  3. Jun 9, 2010 #2

    tiny-tim

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    Hi Telemachus! :smile:
    That's right :smile:, but from then on you're making it too complicated. :redface:

    Hint: Where is the midpoint of the rhombus? :wink:
     
  4. Jun 9, 2010 #3
    On the intersection between L and L', but how should I get L'? I thought maybe using pythagoric equation I could find another vertex, but im not too sure. I know it gives enough data, but I don't know how to use it.
     
  5. Jun 9, 2010 #4
    I had a misunderstood, I think I was on the right way, cause actually I didn't corroborate if A belongs to L, and the sentence don't say so. I'll corroborate, if it doesn't I was on the right way, and it will be easy to solve, cause if A don't belongs to L, it must belongs to L'.

    Bye there, and thanks.
     
  6. Jun 9, 2010 #5

    tiny-tim

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    L' is perpendicular to L, and goes through A. :smile:

    (and remember, you don't need to find L', you only need the midpoint :wink:)
     
  7. Jun 9, 2010 #6
    How could I get the midpoint without L'? I thought of it as the intersection between L and L'.
     
  8. Jun 9, 2010 #7

    tiny-tim

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    AM is on L', so it's perpendicular to L. :wink:
     
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