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Rotations - Concept

Teacher/Instructor Brian McCall
Brian McCall

Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

A rotation is an isometric transformation: the original figure and the image are congruent. The orientation of the image also stays the same, unlike reflections. To perform a geometry rotation, we first need to know the point of rotation, the angle of rotation, and a direction (either clockwise or counterclockwise). A rotation is also the same as a composition of reflections over intersecting lines.

There are 4 types of transformations one of which is rotation. Rotation is an isometry which means the beginning image and the new image are going to be congruent. You need to know 3 key things when you're performing your rotation.
First thing is a point of rotation otherwise you're just going to be rotating in space. Secondly, you need to know an angle of rotation that tells you exactly how far to rotate and last you need a direction, either clockwise or counterclockwise, so to make this little more spefic, I've drawn a little diagram here that shows rotating point a to a prime about point p x degrees counterclockwise, so again the f8need to know is if you have an image or a point where you're going to rotate it about because this distance between your point and where you're rotating needs to be constant or congruent to your new image.
Second thing that you need to know is how many degrees? So you're not going to have x you're going to have a number like 30 so this will be about a 30 degree rotation and last the counterclockwise. If I'd say clockwise we would have rotated it not in this direction but it would have been over here so I guess I could call this a double prime. So a double prime would have been a clockwise rotation x degrees about point p. So again the 3 key things that you need to know when you're performing rotation; the point that you're rotating it about, how much you're rotating and in what direction.

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