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2. 2 G (4, -1) F (-1, 0) A (-5, 5) P (-4, -1) M (0, 5) B (-5, -3) Warm Up

3. Copyright © Ed2Net Learning Inc.3 Lets review what we have learned in our lesson Flip is a transformation in which a plane figure is flipped or reflected across a line, creating a mirror image of the original figure. A flip is also called a reflection. An object and its reflection have the same shape and size, but the figures face in opposite directions.

4. Copyright © Ed2Net Learning Inc.4 The reflection of the point (x, y) across the x-axis is the point (x, -y). The reflection of the point (x, y) across the y-axis is the point (-x, y). The reflection of the point (x, y) across the line y = x is the point (y, x). The reflection of the point (x, y) across the line y = -x is the point (-y, -x). Review

5. Copyright © Ed2Net Learning Inc.5 Let’s get started Rotation: A rotation is a transformation that turns a figure about a fixed point called the center of rotation. An object and its rotation are the same shape and size, but the figures may be turned in different directions. The rotation of an object is called its image. Rotations can occur in either a clockwise or counterclockwise direction.

6. Copyright © Ed2Net Learning Inc.6 Example1 If the original object was labeled with letters, such as polygon ABCDE, the image may be labeled with the same letters followed by a prime symbol, A'B'C'D'E'. This Rotation is 90° counterclockwise

7. Copyright © Ed2Net Learning Inc.7 Example 2 Triangle rotated about point O O A’ B’ C’ A B C

8. Copyright © Ed2Net Learning Inc.8 Rotation notation is usually denoted R( center, degrees ) "Center" is the 'center of rotation.' "Degrees" stands for how many degrees you should rotate. A positive number usually by convention means counter clockwise. The reflection, translation and rotation are congruent transformations. 360 degrees is a full circle of rotation. We use the symbol ° for degrees. A half circle of rotation is 180° and a quarter circle 90° Notation for Rotation

9. Copyright © Ed2Net Learning Inc.9 Rotation by 90° about the origin A rotation by 90° about the origin can be seen in the figure below in which A is rotated to its image A'. The general rule for a rotation by 90° about the origin is (A,B)  (-B, A)

10. Copyright © Ed2Net Learning Inc.10 Rotation by 180° about the origin A rotation by 180° about the origin can be seen in the figure below in which A is rotated to its image A'. The general rule for a rotation by 180° about the origin is (A,B)  (-A, -B)

11. Copyright © Ed2Net Learning Inc.11 Rotation by 270° about the origin A rotation by 270° about the origin can be seen in the figure below in which A is rotated to its image A'. The general rule for a rotation by 270° about the origin is (A,B)  (B, -A).

12. Copyright © Ed2Net Learning Inc.12 Angles in a Rotation In rotation, recognize angles of certain sizes and understand the basic working of a unit circle. Recognize and reproduce the size of a right angle (90 degrees), a 45 degree angle, a 30 degree angle and a 60 degree angle.  90 degrees – right angle  45 degrees - Half a right angle  60 degrees - Two 30 degree angles

13. Copyright © Ed2Net Learning Inc.13 Unit Circle 90° 270° 180° 0°0° 360° Unit circle moves in a counterclockwise direction.

14. Copyright © Ed2Net Learning Inc.14 Your Turn 1)A _______is a transformation that turns a figure about a fixed point called the center of rotation. 2)An object and its rotation are the _____ shape and size. 3)Rotations can occur in either a _________ or _________direction. 4) Rotation notation is usually denoted __. 5) ______ degrees is a full circle of rotation.

15. Copyright © Ed2Net Learning Inc.15 Your Turn 6) _______ is an right angle. 7) _______circle moves in a counterclockwise direction. 8) The rule for a rotation by ______ about the origin is (A,B)  (B, -A). 9) The general rule for a rotation by 90° about the origin is (A,B)  ______. 10) A rotation of 180º is also called a _______ in the origin.

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18. Copyright © Ed2Net Learning Inc.18 1) Rotate the figure 270º about O. Label the image's vertices.

19. Copyright © Ed2Net Learning Inc.19 2) Find the image of the point A (4, 2) in the plane for the given rotations about the rotocenter, O, where O is the origin in the plane. (a) R O, 90 : A → _____.

20. Copyright © Ed2Net Learning Inc.20 3) What is the image of the non-square rectangle ABCD by the rotation R O, −90 ?

21. Copyright © Ed2Net Learning Inc.21 Lets review what we have learned in our lesson An object and its rotation are the same shape and size, but the figures may be turned in different directions. The rotation of an object is called its image. Rotations can occur in either a clockwise or counterclockwise direction. Rotation notation is usually denoted R( center, degrees ) 360 degrees is a full circle of rotation.

22. Copyright © Ed2Net Learning Inc.22 R 90 (x,y) = ( -y, x) R 180 (x, y) = ( -x, -y) R 270 (x,y) = (y, -x) A rotation of 180º is also called a point reflection in the origin. Rotations > 0 are counterclockwise. Rotations < 0 are clockwise. Rotation Angle

23. Copyright © Ed2Net Learning Inc.23 Practice and keep up the good work