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rule for 90° rotation counterclockwise
(x,y)->(-y,x)
rule for 180° rotation
(x,y)->(-x,-y)
rule for 270° rotation counter clockwise
(x,y)->(y,-x)
rule for 360° rotation
(x,y)->(x,y)
rule for reflection across the line y=x
(x,y)->(y,x)
rule for reflection across the line y=-x
(x,y)->(-y,-x)