1 / 20

Rotations

Rotations. Rotations. Rotations. Rotations. Rotations. Rotations. Rotations. Ch 9-3. Rotations. Rotations. rotation. Draw rotated images using the angle of rotation. center of rotation angle of rotation rotational symmetry invariant points direct isometry indirect isometry.

breeve
Télécharger la présentation

Rotations

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. Rotations Rotations Rotations Rotations Rotations Rotations Rotations Ch 9-3 Rotations Rotations

  2. rotation • Draw rotated images using the angle of rotation. • center of rotation • angle of rotation • rotational symmetry • invariant points • direct isometry • indirect isometry • Identify figures with rotational symmetry. Lesson 3 MI/Vocab

  3. Rotations A transformation in which a figure is turned about a fixed point. The fixed point is the Center of Rotation Rays drawn from the center of rotation to a point and its image form an angle called the Angle of Rotation.

  4. Watch when this rectangle is rotated by a given angle measure. Hi Center of Rotation

  5. Angle of Rotation Hi Center of Rotation

  6. A. For the following diagram, which description best identifies the rotation of triangle ABC around point Q? • A • B • C • D A. 20° clockwise B. 20° counterclockwise C. 90° clockwise D. 90° counterclockwise Lesson 3 CYP1

  7. Rotations • A composite of two reflections over two intersecting lines • The angle of rotation is twice the measure of the angle b/t the two lines of reflection • Coordinate Plane rotation Rotating about the origin

  8. Reflections in Intersecting Lines Find the image of parallelogram WXYZ under reflections in line p and then line q. First reflect parallelogram WXYZ in line p. Then label the image W'X'Y'Z'. Next, reflect the image in line q. Then label the image W''X''Y''Z''. Answer: Parallelogram W''X''Y''Z'' is the image of parallelogram WXYZ under reflections in line p and q. Lesson 3 Ex2

  9. In the following diagram, which triangle is the image of ΔABC under reflections in line m and then line n. • A • B • C A. blue Δ B. green Δ C. neither Lesson 3 CYP2

  10. Coordinate Plane Rotation Rotating about the origin • Clockwise vs.Counterclockwise • 90o  Quarter turn • 180o  Half turn (clockwise or counterclockwise) • 270o  Three quarter turn Big Hint!!! If you need to rotate a shape about the origin, • TURN THE PAPER • Write down the new coordinates • Turn the paper back and graph the rotated points.

  11. A’ B’ C’ Example #1 Turn the paper (90o clockwise) • Rotate ABC 90o clockwise about the origin. Write the new coordinates A’ (2, 4) B’ (4, 1) C’ (-1, 3) Turn the paper back and graph the rotated points

  12. A’ B’ C’ Example #2 Turn the paper (180o) • Rotate ABC 180o about the origin. Write the new coordinates A’ (4, -2) B’ (1, -4) C’ (3, 1) Turn the paper back and graph the rotated points

  13. A B D C Rotational Symmetry • A figure has rotational symmetry if it can be mapped onto itself by a rotation of 180º or less. • Equilateral Triangle • Square • Most regular polygons

  14. magnitude of symmetry There are 3 rotations (<360 degrees) where the triangle maps onto itself. The equilateral triangle has rotational symmetry of order = 3. An equilateral triangle maps onto itself every 120 degrees of rotation.

  15. 1 1 1 1 1 1 5 5 5 5 5 5 2 2 2 2 2 2 4 4 4 4 4 4 3 3 3 3 3 3 magnitude of symmetry An regular pentagon has an order of 5.

  16. Use a protractor to measure a 45° angle counterclockwise with as one side. Extend the other side to be longer than AR. Draw a Rotation A. Rotate quadrilateral RSTV45° counterclockwise about point A. • Draw a segment from point R to point A. • Locate point R' so that AR = AR'. • Repeat this process for points S, T, and V. • Connect the four points to form R'S'T'V'. Lesson 3 Ex1

  17. Draw a Rotation Quadrilateral R'S'T'V' is the image of quadrilateral RSTV under a 45° counterclockwise rotation about point A. Answer: Lesson 3 Ex1

  18. Use a protractor to measure a 115° angle clockwise with as one side. Draw Use a compass to copy onto Name the segment Draw a Rotation B. Triangle DEF has vertices D(–2, –1), E(–1, 1), and F(1, –1). Draw the image of DEF under a rotation of 115° clockwise about the point G(–4, –2). First draw ΔDEF and plot point G. Draw a segment from point G to point D. Repeat with points E and F. Lesson 3 Ex1

  19. Draw a Rotation ΔD'E'F' is the image of ΔDEF under a 115° clockwise rotation about point G. Answer: Lesson 3 Ex1

  20. A.B. C. D. B. Triangle ABC has vertices A(1, –2), B(4, –6), and C(1, –6). Draw the image of ΔABC under a rotation of 70° counterclockwise about the point M(–1, –1). • A • B • C • D Lesson 3 CYP1

More Related