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Warm-Up

Learn about rotations in the coordinate plane, reflections over axes, and perform rotations on given points and shapes. Homework questions included.

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Warm-Up

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  1. Warm-Up Reflect triangle ABC across the line y = 1 given A(0,3) , B(-1, 5) , and C(-4, 2). List the coordinates of the image: A’( , ) B’( , ) C’( , ) Put homework questions on the board!

  2. A. B. C. D.

  3. 9.1 Summary Reflect over x-axis (x , y)  Reflect over y-axis (x , y)  Reflect over y=x

  4. 9.3 Rotations • Objectives: • Make rotations about a point in the coordinate plane. • Know the relationship between reflections and rotations.

  5. Clockwise versus Counterclockwise 90° 180° 270° clockwise counterclockwise counterclockwise

  6. P P Rotation about a point. Is a rotation an isometry? angle of rotation image preimage center of rotation

  7. Example 1: Perform the following rotations on point A. Rotate 90 degrees counterclockwise about the origin: Rotate 180 counterclockwise about the origin: Rotate 270 degrees counterclockwise about the origin: A(-2,3) (-3, -2) (2, -3) (3, 2)

  8. Strategies for Rotations: • Measure the angle of rotation • Memorize the rules • Physically rotate your paper

  9. Example 2: DRST has coordinates R(-2, 3), S(0, 4), and T(3, 1). If DRST is rotated 90° counter clockwise about the origin, what are the new coordinates?

  10. Example 3: A quadrilateral ABCD has the following vertices: A(2, -2) B(4, 1), C(5, 1), D(5, -1). Rotate ABCD 270° counterclockwise about the origin and name the coordinates of the new vertices.

  11. Example 4: A quadrilateral has a vertices P(3, -1) Q(4, 0), R(4, 3), and S(2, 4). Rotate PQRS 180°counterclockwise about (0,0) and name the coordinates of the new vertices.

  12. Create your own! • Take your partner’s notes • Draw any polygon on their coordinate plane • Tell them how many degrees to rotate it • Check your partner’s work!

  13. 9.1, 9.3 Summary Reflect over x-axis (x , y) (x, -y) Reflect over y-axis (x , y) (-x, y) Reflect over y=x (x , y) (y , x) Rotate 90 degrees CCW (x, y) (-y, x) Rotate 180 degrees CCW (x, y) (-x, -y) Rotate 270 degrees CCW (x, y) (y, -x)

  14. Triangle PQR is shown below. What is the image of point Q after a 90° counterclockwise rotation about the origin? A. (–5, –4) B. (–5, 4) C. (5, 4) D. (4, –5)

  15. The coordinates of quadrilateral ABCD before and after a rotation about the origin are shown in the table. Find the angle of rotation. A. 90° clockwise B. 90° counterclockwise C. 180° clockwise D. 45° clockwise

  16. Describe the transformations used to map the figure in the left column onto each of the figures in the right column.

  17. 1. Hexagon DGJTSR is shown below. What is the image of point T after a 90 counterclockwise rotation about the origin? 2. The coordinates of triangle XYZ before and after a rotation about the origin are shown in the table. Find the angle of rotation. A. 180° clockwise B. 270° clockwise C. 90° clockwise D. 90° counterclockwise

  18. Homework: p.644-646 #15-18, 37, 39, 40 All rotations are COUNTER CLOCKWISE Geometry

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