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Thread: Please check, Matrix transformation

  1. #1
    Junior Member
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    Please check, Matrix transformation

    A transformation f is a reflction in the line y = -x + 1


    What I have done;

    First I shifted the plane 1 unit down so that the line of reflection passes through the origin. I think the line y = -x makes an angle -45 degrees with the positive x - axis. It then follows that the reflection in this line is Q-45 degrees so that the required matrix is



    Q-45 degrees ( Cos 270 Sin 270 ) = ( 0 -1 )
    Sin270 -cos 270 -1 0

    Then I find the reflection by using composite transformation
    t 0,1 o (q -45 degrees 0 t 0,-1)


    This gives f(x) = (0 -1)x + (1)
    -1 0 1
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by fair_lady0072002
    A transformation f is a reflction in the line y = -x + 1


    What I have done;

    First I shifted the plane 1 unit down so that the line of reflection passes through the origin. I think the line y = -x makes an angle -45 degrees with the positive x - axis. It then follows that the reflection in this line is Q-45 degrees so that the required matrix is



    Q-45 degrees ( Cos 270 Sin 270 ) = ( 0 -1 )
    Sin270 -cos 270 -1 0

    Then I find the reflection by using composite transformation
    t 0,1 o (q -45 degrees 0 t 0,-1)


    This gives f(x) = (0 -1)x + (1)
    -1 0 1
    This looks OK to me. (you can check this by finding the images of a three
    points using a diagram, and checking the observation against the result
    given by the transformation).

    RonL

    RonL
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