ROTATION

12/7/2015 Goals Identify rotations in the plane. Apply rotation to figures on the coordinate plane.

12/7/2015 Rotation A transformation in which a figure is turned about a fixed point, called the center of rotation. Center of Rotation

The center of rotation could be a point outside the shape or on the shape A ROTATION MEANS TO TURN A FIGURE center of rotation

ROTATION A ROTATION MEANS TO TURN A FIGURE The triangle was rotated around the point. center of rotation

ROTATION If a shape spins 360 , how far does it spin? 360 

ROTATION If a shape spins 180 , how far does it spin? 180  Rotating a shape 180  turns a shape upside down.

ROTATION If a shape spins 90 , how far does it spin? 90 

ROTATION Describe how the triangle A was transformed to make triangle B AB Describe the translation. Triangle A was rotated right 90 

ROTATION Describe how the arrow A was transformed to make arrow B Describe the translation. Arrow A was rotated right 180  A B

12/7/2015 Rotation Rays drawn from the center of rotation to a point and its image form an angle called the angle of rotation. Center of Rotation 90  G G’

12/7/2015 A Rotation is an Isometry (Rigid Transformation) Segment lengths are preserved. Angle measures are preserved. Parallel lines remain parallel. Orientation is unchanged.

12/7/2015 Rotations on the Coordinate Plane Be able to do: 90  rotations 180  rotations clockwise & counter- clockwise Unless told otherwise, the center of rotation is the origin (0, 0).

12/7/  clockwise rotation Formula (x, y)  (y,  x) A(-2, 4) A’(4, 2) Or… Use the relation between the slopes of two perpendicular lines

12/7/2015 Rotate (-3, -2) 90  clockwise Formula (x, y)  (y,  x) (-3, -2) A’(-2, 3) Or… Use the relation between the slopes of two perpendicular lines

12/7/  counter-clockwise rotation Formula (x, y)  (  y, x) A(4, -2) A’(2, 4)

12/7/2015 Rotate (-5, 3) 90  counter-clockwise Formula (x, y)  (  y, x) (-3, -5) (-5, 3)

12/7/  rotation Formula (x, y)  (  x,  y) A(-4, -2) A’(4, 2)

12/7/2015 Rotate (3, -4) 180  Formula (x, y)  (  x,  y) (3, -4) (-3, 4)

12/7/2015 Rotation Example Draw a coordinate grid and graph: A(-3, 0) B(-2, 4) C(1, -1) Draw  ABC A(-3, 0) B(-2, 4) C(1, -1)

12/7/2015 Rotation Example Rotate  ABC 90  clockwise. Formula (x, y)  (y,  x) A(-3, 0) B(-2, 4) C(1, -1)

12/7/2015 Rotate  ABC 90  clockwise. (x, y)  (y,  x) A(-3, 0)  A’(0, 3) B(-2, 4)  B’(4, 2) C(1, -1)  C’(-1, -1) A(-3, 0) B(-2, 4) C(1, -1) A’ B’ C’

12/7/2015 Rotate  ABC 90  clockwise. Check by rotating  ABC 90 . A(-3, 0) B(-2, 4) C(1, -1) A’ B’ C’

12/7/2015 Rotation Formulas 90  CW(x, y)  (y,  x) 90  CCW(x, y)  (  y, x) 180  (x, y)  (  x,  y) These rules only work when the center of rotation is the origin. Use the opposite reciprocal relation between the slopes of perpendicular lines to do rotations about other points.

12/7/2015 Rotating segments A B C D E F G H O

12/7/2015 Rotating AC 90  CW about the origin maps it to _______. A B C D E F G H CE O

12/7/2015 Rotating HG 90  CCW about the origin maps it to _______. A B C D E F G H FE O

12/7/2015 Rotating AH 180  about the origin maps it to _______. A B C D E F G H ED O

12/7/2015 Rotating GF 90  CCW about point G maps it to _______. A B C D E F G H GH O

12/7/2015 Rotating ACEG 180  about the origin maps it to _______. A B C D E F G H EGAC AE C G O

12/7/2015 Rotating  FED 270  CCW about point D maps it to _______. A B C D E F G H  BOD O

12/7/2015 Summary A rotation is a transformation where the preimage is rotated about the center of rotation. Rotations are Rigid Transformations

12/7/2015

Homework