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Math Help - Transformation matrix (one triangle to another).

  1. #1
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    Transformation matrix (one triangle to another).

    Hello,
    I have made this account purely to find the way to answer this question, I have asked my maths teacher and he couldn't answer, so please can anyone answer it to me? thank you

    The question I need to answer is the (b) section, please show me the working and explain it like you would to a five year old....

    according to the mark scheme, the answer is:

    0 -1
    -1 0

    and

    1 0
    0 2

    (the answers are matrices)
    please answer asap, I have attached the question
    thanks
    Attached Files Attached Files
    Last edited by mr fantastic; April 16th 2011 at 02:57 PM. Reason: Re-titled.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Hint for (b) (i):

    Notice that the transformation f which maps T onto S is a symmetry with respect to r : x + y = 0 .

    Try (b) (ii).
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  3. #3
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    thanks for replying :-) , but I don't understand, do you mean T onto R? and how does that help me to find the required 2 by 2 matrix to map the triangle.
    in the mark scheme it said that I would get one mark for showing simutaneous equations, but I have no idea what simutaneous equations have to do with the question...... can you please tell me the method to find the matrix? thanks
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  4. #4
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    For T -> R, it is clear from the diagram that (x,y) -> (-y,-x).
    What matrix does that?
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  5. #5
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    thats a good method! thanks.
    so, just a recab (please correct me if I am wrong)
    x and y are switched and they both become into negatives, and to do that the matrix :

    0 -1
    -1 0

    is used, ok, now I have an idea how to solve these kind of questions, but in other occasions, it is harder to guess the matrix, in b(ii), for example, point (-6, 2) became ( -6, 4) , so x remains the same and y is doubled, but how do I guess the matrix now?
    thanks
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  6. #6
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by IBstudent View Post
    do you mean T onto R?

    Right, it was a typo.
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