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)

90° - ONE TURN

180° - TWO TURNS

270° - THREE TURNS

On the Coordinate Plane

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’ __________

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

R’ __________

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

R’ __________

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

R’ __________

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

R’ __________

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

R’ __________

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˚ →

Rotate (4, -2) 90˚ →

Rotate (4, -2) 180˚ →

Rotate (4, -2) 270˚ →