Reflection and Rotation
Date: 02/20/2003 at 10:57:36 From: Anita Bechtold Subject: Reflection and rotation I am a math teacher. I have a strong math background but not for these topics. Can rotation of a figure and reflection of that same figure yield the same result at times? If a shape with one line of symmetry, such as a club (from playing cards), is reflected across a line, this same image could be obtained by rotating the shape, right?
Date: 02/20/2003 at 12:30:45 From: Doctor Peterson Subject: Re: Reflection and rotation Hi, Anita. I think you are talking about something like this: Here I drew a T and an L, and reflected both across a line. The image of the L clearly can be obtained only by reflection; but the T image can also be obtained by rotation about a point on the line, as shown. The reason for this is that any rotation or translation is equivalent to two reflections; when the object has a reflection symmetry, a single reflection produces the same effect as that reflection followed by a reflection in its line of symmetry, and so is equivalent to a rotation; specifically, it will be a rotation about the point of intersection of the line in which it was reflected, and the line of symmetry (of both the original object and the image). So if a problem asks for any transformation that will take the first T into the other, you can use either the reflection or the rotation. Of course, if the corresponding points on the original and the image were marked, that would force you to choose either the reflection or the rotation. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Date: 02/20/2003 at 14:55:48 From: Anita Bechtold Subject: Thank you (reflection and rotation ) Wow! That was a prompt response! Thank you so much. I especially like the illustration. Yes, that's exactly what I meant. You were very helpful.
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