Question by Andrew W: Explain how any translation can be replaced by a reflection about two parallel lines?
Two students were discussing the four types of transformations they had learned: reflections, rotations, translations, and glide reflections. They noticed that reflections about two parallel lines seemed to produce a translation. Please help me explain.
Answer by dudette
okay. let’s take the example of the x-axis (which is also y=0) and the line y=1.they are parallel lines.reflect the line y=1 about the x-axis and you get y= -1.it is a reflection about the x-axis, and also a translation of 2 units in the negative y-direction, i.e. replacing y with -y is equivalent to replacing y with y+2…—> the line y = 1reflection: -y = 1y = -1translation:y + 2 = 1y = 1 – 2y = -1same applies for the reflection about any early 2 parallel lines.i hope this makes sense! :)good luck.
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