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

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 opposite direction of a clock (unless told otherwise)

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

90˚ Center of Rotation (0, 0)

180˚

270˚

Rotating about a Center Point Full circle = 360˚ 360÷5 72˚

R(2, 5) 90° Rotation about the origin

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

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

R(4, 3) 90° rotation about point (2, 2)

R(4, 3) 180° rotation about point (2, 2)

R(4, 3) 270° rotation about point (2, 2)

90° rotation about the origin

270° rotation about the origin

180° rotation about the point (-4, 2)

Ex 3) 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: _______

You Try! 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: ________

Ex 4) 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 ?________

You Try! Determine 3 angles of rotation that would map a regular octagon back onto itself.

Point Symmetry?

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˚ →

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)