Rules for Transformations on a Coordinate Plane

Translations: one type of transformation where a geometric figure is “slid” horizontally, vertically, or both. Sliding a polygon to a new position without turning it. When translating a figure, every point of the original figure is moved the same distance and in the same direction. Reflections: A type of transformation where a figure is “flipped” over a line of symmetry. A reflection produces a mirror image of a figure.

Reflect a figure over the x-axis

change the y-coordinates to their opposites. (x, y) → (x, -y)

Reflect a figure over the y-axis

Reflect a figure over the y-axis: change the x-coordinates to their opposites. (x, y) → (-x, y)

Reflect a figure over the y = x

change the coordinate positions (x, y) → (y, x)

Reflect a figure over the y = -x

change the coordinate positions & signs (x, y) → (-y, -x)

90° clockwise rotation

(x, y) → (y, -x)

90° counter-clockwise rotation

(x,y) → (-y,x)

180° rotation

(x, y) → (-x, -y)

270° clockwise rotation

(x, y) → (-y, x)