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### Rotation, Translation, and Reflection in the Plane

```Date: 12/11/2005 at 14:05:18
From: Taylor
Subject: what do these math terms mean?

Dear Dr. Math,

rotate
translate
reflect

I know they have to do with geometry but I don't know how exactly.

```

```
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/
```
Associated Topics:
High School Symmetry/Tessellations

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