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Math Help - transformation

  1. #1
    Member Veronica1999's Avatar
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    transformation

    A quarter turn is a 90 degree rotation. If the counterclockwise quarter-turn centered at (3,2) is applied to (7,1) what are the coordinates of the image? What are the image coordinates when this transformation is applied to a general point (x,y)?

    I have (4,6) but i can't get the second one.

    Pls find attached work.i have found a vector pattern for the transformation
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  2. #2
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    Hello, Veronica1999!

    A quarter turn is a 90 degree rotation.
    If the counterclockwise quarter-turn centered at (3,2) is applied to (7,1),
    . . what are the coordinates of the image?
    What are the image coordinates when this transformation
    . . is applied to a general point (x,y)?

    We have the point A(3,2) and any point P(x,y)

    Code:
          |                 y-2
          |             Q * - - *
          |                     :
          |                     :
          |                     : x-3
          |                     :
          |                     :
          |                     :P
          |                     *(x,y}
          |                 *   :
          |             *       :y-2
          |         *           :
          |   A * - - - - - - - *
          |   (3,2)   x-3
        --+------------------------
          |

    Going from A to P, we move x\!-\!3 units right and y\!-\!2 up.

    Going from P to Q, we move x\!-\!3 units up and y\!-\!2 left.
    . . (I hope you understand why.)

    Therefore, point Q is at: . (x\!-\!y\!+\!2,\:x\!+\!y\!-\!3)

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