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(x, y) → (x + a, y + b)
Translation
(x, y) → (x, -y)
Reflection across the x-axis
(x, y) → (-x, y)
Reflection across the y-axis
(x, y) → (y, x)
Reflection across the line y=x
(x, y) → (-y, x)
Rotation 90° about the origin
(x, y) → (-x, -y)
Rotation 180° about the origin
(x, y) → (y, -x)
Rotation 270° about the origin
(x, y) → (kx, ky)
Dilation with respect to the origin and scale factor of k