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Math Help - Conic Rotation

  1. #1
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    Conic Rotation

    Hi

    Please help me. I want to know how to find the coordinates of a circle after they have been rotated some degrees.

    One problem I read wrote this:

    "Shown in the standard (x,y) coordinate plane below, pint P (6,6) is rotated 90 degrees clockwise about the orgin (2,3). What are the coordinates of P after the rotation has been complete?"

    I know the answer is (5,-1), but I don't know why that is the answer or how to solve the problem for other questions!
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  2. #2
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    Hello klaus113

    Welcome to Math Help Forum!
    Quote Originally Posted by klaus113 View Post
    Hi

    Please help me. I want to know how to find the coordinates of a circle after they have been rotated some degrees.

    One problem I read wrote this:

    "Shown in the standard (x,y) coordinate plane below, pint P (6,6) is rotated 90 degrees clockwise about the orgin (2,3). What are the coordinates of P after the rotation has been complete?"

    I know the answer is (5,-1), but I don't know why that is the answer or how to solve the problem for other questions!
    Think about any point whose coordinates are (x_1,y_1) - see the attached diagram. Its horizontal and vertical distances from (2, 3) are x_1-2 and y_1-3, respectively. After a rotation through 90^o clockwise about this point, these will be the vertical distance below and the horizontal distance to the right of this point.

    So the coordinates of the image of (x_1,y_1) after this rotation are
    (2+y_1-3, 3 -[x_1-2]); i.e. (y_1-1, 5-x_1)
    This gives the general formula you're looking for, and confirms that (6,6) \mapsto (5, -1).

    Grandad
    Attached Thumbnails Attached Thumbnails Conic Rotation-untitled.jpg  
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  3. #3
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    Hello, klaus113!

    Point P(6,6) is rotated 90 clockwise about the point Q(2,3).
    What are the coordinates of P after the rotation is completed?
    A sketch is always a good idea . . .
    Code:
            |         P
            |           o (6,6)
            |           :
            |           :3
            | Q o - - - +
            |(2,3)  4
            |
        ----+-----------------
            |
    Going from Q to P, we move 4 right and 3 up.


    Code:
            |
            |(2,3) 3 
            | Q o - - +
            |         :
            |         :4
        ----+---------:----
            |         o P'
            |
    Going from Q to P', we move 3 right and 4 down.
    . .
    Do you see why?

    Now we know the location of P'.

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