For a given line L, let Ω l ( x ) be the relectoin of point X with respect to line L. Ω l ( x ) = X if and only if X is in L. This is what I did but I don't think you can do what I did. Ω l ( x ) = X d ( Ω l ( x ) , X ) = 0 d ( X , Ω l ( x ) ) = X = Ω l ( x )

Question

For a given line L, let       Ω          l        (  x  )  be the relectoin of point X with respect to line L.         Ω          l        (  x  )  =  X   if and only if X is in L.    This is what I did but I don&#039;t think you can do what I did.         Ω          l        (  x  )  =  X    d  (      Ω          l        (  x  )  ,  X  )  =  0    d  (  X  ,      Ω          l        (  x  )  )  =  X  =      Ω          l        (  x  )

minotaurafe · Accepted Answer

We have to prove that,        Ω    L    (  X  )  =  K   if and only if Xis in L     First suppose that,   (  K  )  =  X     the distance between       Ω    L    (  X  )   and   X  ,    ⇒  d  (      Ω    L    (  X  )  X  )  =  d  (  X  ,  X  )    =  0    ⇒  X   lies in   L  .    Conversely, suppose that Xlies in L    ⇒  the reflecti on of   X  w  .  r  .  t  .  L  ,      Ω    L    (  X  )   also lies in    ⇒  (      Ω    L    )  =  X  .    Therefore,       Ω    L    (  X  )  =  X   if and only if   X   is in   L

For a given line L, let Omega _{l}(x) be the relectoin of point X with respect to line L. Omega _{l}(x)=X if and only if X is in L.

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