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Math Help - Rotation of points

  1. #1
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    Rotation of points

    In the standard (x, y) coordinate plane, the coordinate of D are (d, k) and the coordintate of E are (e, k). When D is roated 180 degrees about E the result is F. In terms of d, e, and k, what are the coordinates of F?

    The answer is (2e - d, k) but I'm not sure to obtain to it
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    E is the middle point of DF i.e, if F=(x,y) then,

    (e,k)=\left(\dfrac{x+d}{2},\dfrac{y+k}{2}\right)

    Fernando Revilla
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    Quote Originally Posted by FernandoRevilla View Post
    E is the middle point of DF i.e, if F=(x,y) then,

    (e,k)=\left(\dfrac{x+d}{2},\dfrac{y+k}{2}\right)

    Fernando Revilla
    Hmm I still don't quite understand how that helps, can you elaborate some more?
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by sarahh View Post
    Hmm I still don't quite understand how that helps, can you elaborate some more?
    e=\dfrac{x+d}{2}\Leftrightarrow 2e=x+d \Leftrightarrow x=2e-d

    k=\dfrac{y+k}{2}\Leftrightarrow 2k=y+k \Leftrightarrow y=k


    Fernando Revilla
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