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reflection over x-axis
(x,y)→(x,-y)
reflection over y-axis
(x,y)→(-x,y)
reflection over y=x
(x,y)→(y,x)
translation by some vector
(x,y)→(x+a,y+b)
90 degree counter clockwise rotation (270 degree clockwise rotation)
(x,y)→(-y,x)
180 degree rotation counter clockwise or clockwise
(x,y)→(-x,-y)
270 degree rotation counter clockwise or a 90 degree clockwise rotation
(x,y)→(y,-x)