RotationsA turn around a center.

The distance from the center to any point on the shape stays the

same.

Clockwise

Rotations degrees & direction

Rotation of 90°:    

Rotation of 180°:   

Rotation of 270°:     

A rotation turns a figure through an angle about a fixed point called the center.  It is a rigid isometry. Rules of rotation are for clockwise rotations.

Counter clockwise rotations are opposite clockwise.90°cw = 270°ccw and 270°cw = 90°ccw

𝑹𝟗𝟎°𝒄𝒘 (𝒙 , 𝒚 )=(𝒚 , −𝒙 )

𝑹𝟏𝟖𝟎°𝒄𝒘 (𝒙 , 𝒚 )=(− 𝒙 , −𝒚 )

𝑹𝟐𝟕𝟎°𝒄𝒘 (𝒙 , 𝒚 )=(− 𝒚 ,𝒙)

N(1, -4) N'(-4, -1)

(270 ° CCW rotation)

T’

N’

S’

Rotate ∆TSN 90°cw

(x, y) (y, -x)

T(-1, 1) T'(1, 1)

S(4, -1) S'(-1, -4)

T(-1, 1) T'(1, -1)S(4, -1) S'(-4, 1)N(1, -4) N'(-1, 4)

Rotate ∆TSN 180°

(x, y) (-x, -y)

T(-1, 1) T'(-1, -1)S(4, -1) S'(1, 4)

N(1, -4) N'(4, 1)

Rotate ∆TSN 270° cw

(x, y) to (-y, x)

Rotate 90 CW about the Origin

(Same as 270 CCW)

Change the sign of x and switch the order

x,y y, x

Rotate 90 CW

Rotate 270 Clockwise(Same as 90 ccw)

Change the sign of y and switch the order

x,y y,x

Rotate 90° counterclockwiseabout the origin

E( 3, 2) ( , )

F( 6, 5) ( , )

G(0, 2) ( , )

Rotate 90° counterclockwiseabout the origin

E( 3, 2) E' 2, 3

F( 6, 5) F' 5, 6

G(0, 2) G ' 2,0

Rotate 180 about the Origin

ONLY Change the signs

,,y yx x

Rotate 180° about the origin

Rotate 180° about the origin

Q( 8, 2) Q ' 8,2

R( 8, 9) R' 8,9

S( 2, 2) S' 2,2

T( 2, 9) T' 2,9

Rotation of 90°:    

Rotation of 180°:   

Rotation of 270°:     

A rotation turns a figure through an angle about a fixed point called the center.  It is a rigid isometry. Rules of rotation are for clockwise rotations.

Counter clockwise rotations are opposite clockwise.90°cw = 270°ccw and 270°cw = 90°ccw

𝑹𝟗𝟎°𝒄𝒘 (𝒙 , 𝒚 )=(𝒚 , −𝒙 )

𝑹𝟏𝟖𝟎°𝒄𝒘 (𝒙 , 𝒚 )=(− 𝒙 , −𝒚 )

𝑹𝟐𝟕𝟎°𝒄𝒘 (𝒙 , 𝒚 )=(− 𝒚 ,𝒙)

Virtual Nerd Tutoring Lessons

http://www.virtualnerd.com/pre-algebra/geometry/transformations-symmetry/define-transformations/rotation-definition

Lesson on Rotations

http://www.virtualnerd.com/pre-algebra/geometry/transformations-symmetry/rotating-figures/rotate-90-degrees-about-origin

Lesson on Rotations 90°

http://www.virtualnerd.com/pre-algebra/geometry/transformations-symmetry/rotating-figures/rotate-180-degrees-about-origin

Lesson on Rotations 180°

Coordinate Rules for Rotations about the origin: When a point (x, y) is rotated clockwise about the origin, the following rules are true: For a rotation of 900(x, y) (y, -x).For a rotation of 1800 (x,y) (-x, -y). For a rotation of 2700 (x,y) (-y, x).

When a point (x, y) is rotated counterclockwise about the origin, the following rules are true: For a rotation of 900 (x,y) (-y, x).For a rotation of 1800 (x,y) (-x, -y).For a rotation of 2700 (x, y) (y, -x).