Rotations Rotation a transformation that moves an object

Rotations Rotation - a transformation that moves an object around a fixed point that is called the centre of rotation Centre of rotation - the point about which an object is rotated When working in the coordinate plane, assume the center of rotation to be the origin (0, 0) unless told otherwise. Rotation Mapping Rules Original New Point (After Rotation) 90 o CW (or 270 o CCW) (x, y) (y, -x) 180 o CW (or 180 o CCW) (x, y) (-x, -y) 270 o CW (or 90 o CCW) (x, y) (-y, x)

Ex: Rotate the rectangle 90° clockwise, 90° counter-clockwise, and 180° using the origin as the centre of rotation. The coordinates of the vertices for a 90° clockwise rotation will change as follows: Mapping Rule = (x, y) → (y , -x) A (2, 2) → A’ (2, -2) B (5, 2) → B’(2, -5) C (5, 4) → C’(4, -5) D (2, 4) → D’(4, -2)

The coordinates of the vertices for a 90° counter clockwise rotation will change as follows: Mapping Rule = (x, y) → ( -y , x ) A (2, 2) → A’ (-2, 2) B (5, 2) → B’ (-2, 5) C (5, 4) → C’ (-4, 5) D (2, 4) → D’ (-4, 2) The coordinates of the vertices for a 180° rotation will change as follows: Mapping Rule = (x, y) → ( -x, -y ) A (2, 2) → A’ (-2, -2) B (5, 2) → B’ (-5, -2) C (5, 4) → C’ (-5, -4) D (2, 4) → D’ (-2, -4)

Plot the rotated rectangles on the grid.