Translations
(x + a, y + b)
Reflection over the y-axis
(-x, y)
Reflection over the x-axis
(x, -y)
Reflection over y = x
(y, x)
Reflection over y = -x
(-y, -x)
Rotation 90 degrees counterclockwise
(-y, x)
Rotation 90 degrees clockwise
(y, -x)
Rotation 180 degrees
(-x, - y)