How do we review transformations?

Isometry

- length is preserved

- sides are congruents ( like their reflecting)

Ex:                         

              

Direct isometry 

- orientation is preserved( stays the same)

-  The order of the lettering in the figure and the images are the same 

- either clockwise becomes counter clockwise or counter clockwise becomes clockwise 

- every translation and rotation is a direct isometry

Ex: 

Opposite isometry

- orientation isn't preserved (changes)

-  the order of the lettering is reversed

- every reflection and glide reflection is an opposite isometry 

 Ex:

Same orientation :

 rorgin (x,y) -> (-x,-y)              

 R90 (x,y) -> (-y,x)

 R180 ( x,y)-> (-x,-y)

 R270 ( x,y) -> ( y,-x)

Reversed orientation:

 r- x-axis (x,y) -> ( x,-y)

 r-y-axis (x,y) ->(-x,y)

ry = x (x,y) -> ( y,x)

ry = -x (x,y) -> (-y,-x)

Practice question : What is the difference between a direct and opposite isometry?

                                                      Citations 

- http://zsolania.blogspot.com/

- Haskell , Kenn, Functional Lens , http://www.kennknowles.com/blog/2007/12/03/calculating-the-reflect-rotate-translate-normal-form-for-an-isometry-of-the-plane-in-haskell-and-verifying-it-with-quickcheck/