Reflection is not a collineation

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Could you give me a collineation that proves that you can't construct the reflection of a line $e$ across a parallel line $f$ with a straightedge only? (That is, a collineation that maps $e$ and $f$ to parallel lines but where the image of the refelction of $e$ is not the same as the reflection of the image of $e$ across the image of $f$.)