Rotation, Translation, and Reflection in the PlaneDate: 12/11/2005 at 14:05:18 From: Taylor Subject: what do these math terms mean? Dear Dr. Math, Can you please help me? I don't know what these terms mean. rotate translate reflect I know they have to do with geometry but I don't know how exactly. Thanks for your help! Date: 12/11/2005 at 22:59:38 From: Doctor Peterson Subject: Re: what do these math terms mean? Hi, Taylor. There are three ways you can move an object around in a plane without changing its shape or size. (The technical term for this is "isometry".) A rotation means turning it, like +---+ | | | | +-----------+ | | -----> | | | +---+ | +-------+ | | | | +-------+ +---+ Imagine sticking a pin in the object and spinning it by some amount. A translation just slides it, without turning: +---+ | | | | +---+ | | -----> | | | +---+ | | | | | | +-------+ | +---+ | | +-------+ A reflection is like looking at it in a mirror; it flips the object over: +---+ +---+ | | | | | | | | | | -----> | | | +---+ +---+ | | | | | +-------+ +-------+ The "image" will be on the other side of the "mirror" line, the same distance away: +---+ | +---+ | | | | | | | | | | | | | | | | +---+ | +---+ | | | | | | +-------+ | +-------+ See these pages for the same ideas in different words: Translation, Reflection, Rotation http://mathforum.org/library/drmath/view/57839.html Reflection and Rotation http://mathforum.org/library/drmath/view/62267.html If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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