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.

Ishaan Booker 2022-07-27 Answered
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 )
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Answers (1)

minotaurafe
Answered 2022-07-28 Author has 22 answers
 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
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