Rotations EQ: How do you rotate a figure 90, 180 or 270 degrees around a given point?

Rotations Center of Rotation: the point you turn the object around Angle of Rotation: number of degrees to turn the object Counter clockwise: always turn to the left (unless it says otherwise)

On the Coordinate Plane 90° - ONE TURN 180° - TWO TURNS 270° - THREE TURNS

90˚ Center of Rotation (0, 0)

180˚

270˚

Rotating Polygons about their Center Full circle = 360˚ 360÷5 72˚

R(2, 5) a) 90° Rotation about the origin

R(2, 5) b) 180° Rotation about the origin

R(2, 5) c) 270° Rotation about the origin

R(-4, 2) a) 90° Rotation about point O

R(-4, 2) b) 180° Rotation about point O

R(-4, 2) c) 270° Rotation about point O

90˚

180˚

270˚

4.) Point R is the center of regular quadrilateral MATH. # of sides: ________Degree of each turn: _________ a. 90° rotation of H about R # of turns: _____ Image: ______

b. 180° rotation of M about R # of turns: ______ Image: ______ c. 270° rotation of about R # of turns: ________ Image: ________ d. 360° rotation of about R # of turns: _______ Image: _______

5.) Point T is the center of regular decagon ABCDEFGHIJ # of sides: ______ Degree of each turn: _____ a. 72° rotation of H about T # of turns: _____ Image: _____

b. 180° rotation of D about T # of turns: _______ Image: _______ c. 252° rotation of about T # of turns:_______ Image: _______ d. 360° rotation of about R # of turns: _______ Image: ________

6.) Point M is the center of the regular hexagon. # of sides: ________ Degree of each turn: _________ a. What is the angle of rotation that maps H to X?____

b. What is the angle of rotation that maps E to G?______ c. What is the angle of rotation that maps to ?________   d. What is the angle of rotation that maps to ?________

Challenge: Perform the following transformations on the figure below. 1. Reflect over the y-axis 2. (x , y) → (x + 1, y – 8) 3. Rotate 270° about the origin

In a coordinate plane, find the reflection of (2,−4) over the line y = x.            F (−4,2) G (4,2) H (−2,4) J (4,−2)

70° Rotation 70°

90° Rotation 90°

120° Rotation 120°

180° Rotation 180°

270° Rotation 270°

Rules A point (x, y) that has been rotated 90˚ (x, y)→(-y, x) 180˚ (x, y)→(-x, -y) 270° (x, y) → (y, -x)

Practice Rotate (1, 5) 90˚ → Rotate (1, 5) 180˚ → Rotate (1, 5) 270˚ →