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R_{x}=
 [1 0]
 [0 1]
 (x',y')  (x, y)

R_{y}=
 [1 0]
 [ 0 1]
 (x', y')  (x, y)

R_{y= x}=
 [0 1]
 [1 0]
 (x', y')  (y, x)

R_{0,90}=
 [0 1]
 [1 0]
 (x', y')  (y,x)

R_{o, 180}
 [1 0]
 [0 1]
 (x', y')  (x, y)

R_{o, 270}
 [ 0 1]
 [1 0]
 (x', y')  (y, x)

Rotations
If P isn't the center then PO = P'O and m< POP' = angle of rotation

A ______ can be expressed as a composition of 2 reflections over 2 parallel lines
Translation

A _______ can be expressed a a composition of 2 relections over 2 intersecting lines
Rotation

Line Symmetry
there exists a line k such that R_{k }maps the figure onto itself

Point Symmetry
there exists a point O such that H_{o }maps the figure onto itself

Translational symmetry
there exists a translation that maps a figure onto itself

