Tuesday, April 23, 2013

Valley of Translations, Rotations, Reflections, and Glide

Translation

Translation

In Geometry, "Translation" simply means Moving ...
... without rotating, resizing or anything else, just moving.
. Every translation has a direction and a distance.

 
 
To Translate a shape:
Every point of the shape must move:
  • the same distance
  • in the same direction.
     


Writing it out

Example: if we want to say that the shape gets moved 30 Units in the "X" direction, and 40 Units in the "Y" direction, we can write:
This says "all the x and y coordinates will become x+30 and y+40"


Rotation

"Rotation" means turning around a center:

To rotate an object means to turn it around. Every rotation has a center and an angle.


Reflection

To reflect an object means to produce its mirror image. Every reflection has a mirror line. A reflection of an "R" is a backwards "R".

Glide Reflection

A glide reflection combines a reflection with a translation along the direction of the mirror line. Glide reflections are the only type of symmetry that involve more than one step.

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