1 / 25

Geometry

Learn how to identify rotations in the plane and apply rotation formulas to figures on the coordinate plane. Understand the concept of center of rotation and the angle of rotation. Explore 90°, 180°, and 270° rotations in both clockwise and counterclockwise directions.

larochelle
Download Presentation

Geometry

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Geometry Transformations - Rotations

  2. Goals • Identify rotations in the plane. • Apply rotation formulas to figures on the coordinate plane.

  3. 4-3 Rotation • A transformation in which a figure is turned about a fixed point, called the center of rotation. Center of Rotation

  4. 4-3 Rotation • Rays drawn from the center of rotation to a point and its image form an angle called the angle of rotation. G 90 Center of Rotation G’

  5. 4-3 Rotation

  6. A Rotation is an Isometry • Segment lengths do not change. • Angle measures do not change. • Parallel lines remain parallel.

  7. 4-3 Rotation

  8. 4-3 Rotation

  9. Rotations on the Coordinate Plane • Know the formulas for: • 90 rotations • 180 rotations • 270 rotations • clockwise & counter-clockwise Unless told otherwise, the center of rotation is the origin (0, 0).

  10. 90 clockwise rotation Formula (x, y)  (y, x) A(-2, 4) A’(4, 2)

  11. Rotate (-3, -2) 90 CW Formula (x, y)  (y, x) A’(-2, 3) (-3, -2)

  12. 90 counter-clockwise rotation Formula (x, y)  (y, x) A’(2, 4) A(4, -2)

  13. Rotate (-5, 3) 90 counter-clockwise Formula (x, y)  (y, x) (-5, 3) (-3, -5)

  14. 180 clockwise rotation Formula (x, y)  (x, y) A’(4, 2) A(-4, -2)

  15. Rotate (3, -4) 180CW Formula (x, y)  (x, y) (-3, 4) (3, -4)

  16. Rotation Example B(-2, 4) Draw a coordinate grid and graph: A(-3, 0) B(-2, 4) C(1, -1) Draw ABC A(-3, 0) C(1, -1)

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

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

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

  20. Rotation Formulas • 90 CW (x, y)  (y, x) • 90 CCW (x, y)  (y, x) • 180 CW (x, y)  (x, y) • 270 CCW (x, y)  (y, x)

  21. Rotational Symmetry • A figure can be mapped onto itself by a rotation of 180 or less. 45 90 The square has rotational symmetry of 90.

  22. Does this figure have rotational symmetry? The hexagon has rotational symmetry of 60.

  23. Does this figure have rotational symmetry? Yes, of 180.

  24. Does this figure have rotational symmetry? 90 180 270 360 No, it required a full 360 to map onto itself.

  25. Summary • A rotation is a transformation where the preimage is rotated about the center of rotation. • Rotations are Isometries. • A figure has rotational symmetry if it maps onto itself at an angle of rotation of 180 or less.

More Related