1. Homework
Monday 5/23: Rotation of Shapes page 1

2. Rotation of Shapes about an Origin (0,0)

3. Can you suggest any other examples?
Rotation
Which of the following are examples of rotation in real life?
Opening a door?
Walking up stairs?
Riding on a Ferris wheel?
Bending your arm?
Opening your mouth?
Opening a drawer?
Anything that is fixed at a point and turns about that point is an example of a rotation. This is true even if a complete rotation cannot be completed, such as your jaw when opening your mouth.
Can you suggest any other examples?

4. Rotation Vocabulary
Rotation – transformation that turns every point of a pre-image through a specified angle and direction about a fixed point.
image
Pre-image
rotation
fixed point

5. A Rotation is an Isometry
Segment lengths are preserved.
Angle measures are preserved.
Parallel lines remain parallel.
Orientation is unchanged.
9/21/2018

6. Rotation
In order to rotate an object we need 3 pieces of information
Center of rotation
Angle of rotation (degrees)
Direction of rotation

7. Rotation Vocabulary
Center of rotation – fixed point of the rotation. It can be any point on the coordinate plane
Center of Rotation

8. Rotation G 90 Center of Rotation G’
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’
9/21/2018

9. Rotation Vocabulary
Angle of rotation – angle between a pre-image point and corresponding image point. It will be in degrees (basic degrees that we will focus: 90 degrees, 180 degrees, and 270 degrees)
image
Pre-image
Angle of Rotation

10. Rotation Vocabulary
Direction of rotation– it will be counter-clockwise or clockwise

11. Rotation Example: Click the triangle to see rotation
Center of Rotation
Rotation

12. Example 1: Identifying Rotations
Tell whether each transformation appears to be a rotation. Explain. B. A.
No; the figure appears
to be flipped.
Yes; the figure appears
to be turned around a point.

13. Your Turn: Tell whether each transformation appears to be a rotation.
Yes, the figure appears to be turned around a point.
No, the figure appears to be a translation.

14. y x A Rotation of 90° Anticlockwise about (0,0) 8 7 6 C(3,5) 5 1 2 3 4 5 6 7 8
–7 –6 –5 –4 –3 –2 –1 -1 -2 -3 -4 -5 -6
A Rotation of 90° Anticlockwise about (0,0)
(x, y)→(-y, x) x x x
C(3,5) x
B’(-2,4)
C’(-5,3)
B(4,2)
A’(-1,2)
A(2,1) x

15. y x 1 2 3 4 5 6 7 8
–7 –6 –5 –4 –3 –2 –1 -1 -2 -3 -4 -5 -6
A Rotation of 180° about (0,0)
(x, y)→(-x, -y) x x x x
C(3,5) x
B(4,2) x
A(2,1) x x
A’(-2,-1)
B’(-4,-2)
C’(-3,-5)

16. Rotations on the Coordinate Plane
Know the formulas for:
90 rotations
180 rotations
clockwise & counter-clockwise
Unless told otherwise, the center of rotation is the origin (0, 0).
9/21/2018

17. 90 clockwise rotation Formula (x, y)  (y, x) A(-2, 4) A’(4, 2)
9/21/2018

18. Rotate (-3, -2) 90 clockwise
Formula
(x, y)  (y, x)
A’(-2, 3)
(-3, -2)
9/21/2018

19. 90 counter-clockwise rotation
Formula
(x, y)  (y, x)
A’(2, 4)
A(4, -2)
9/21/2018

20. Rotate (-5, 3) 90 counter-clockwise
Formula
(x, y)  (y, x)
(-5, 3)
(-3, -5)
9/21/2018

21. 180 rotation
Formula
(x, y)  (x, y)
A’(4, 2)
A(-4, -2)
9/21/2018

22. Rotate (3, -4) 180 Formula (x, y)  (x, y) (-3, 4) (3, -4)
9/21/2018

23. Rotation Example Draw a coordinate grid and graph: A(-3, 0) B(-2, 4)
Draw ABC
A(-3, 0)
C(1, -1)
9/21/2018

24. Rotation Example Rotate ABC 90 clockwise. Formula (x, y)  (y, x)
9/21/2018

25. 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’ B’
A(-3, 0) C’
C(1, -1)
9/21/2018

26. Rotate ABC 90 clockwise.
Check by rotating ABC 90. A’ B’
A(-3, 0) C’
C(1, -1)
9/21/2018

28. Rotation in a Coordinate Plane

29. Checkpoint
Rotations in a Coordinate Plane
Sketch the triangle with vertices A(0, 0), B(3, 0), and C(3, 4). Rotate ∆ABC 90° counterclockwise about the origin. Name the coordinates of the new vertices A', B', and C'. 4.
A'(0, 0), B'(0, 3), C'(–4, 3)
ANSWER

30. Rotations on a coordinate grid
The vertices of a triangle lie on the points A(2, 6), B(7, 3) and C(4, –1). 7
A(2, 6) 6 5
B(7, 3) 4 3
C’(–4, 1) 2
Rotate the triangle 180° clockwise about the origin and label each point on the image. 1 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 –1 –2
C(4, –1) –3 –4
What do you notice about each point and its image?
B’(–7, –3)
Pupils should notice that when a shape is rotated through 180º about the origin, the x-coordinate of each image point is the same as the x-coordinate of the the original point × –1 and the y-coordinate of the image point is the same as the y-coordinate of the original point × –1. In other words the coordinates are the same, but the signs are different. –5 –6
A’(–2, –6) –7

31. Rotations on a coordinate grid
The vertices of a triangle lie on the points A(–6, 7), B(2, 4) and C(–4, 4). 7
B(2, 4) 6 5
C(–4, 4) 4 3
B’(–4, 2) 2
Rotate the triangle 90° anticlockwise about the origin and label each point in the image. 1 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 –1 –2 –3 –4
What do you notice about each point and its image?
Pupils should notice that when a shape is rotated through 90º anticlockwise about the origin, the x-coordinate of each image point is the same as the y-coordinate of the the original point × –1. The y-coordinate of the image point is the same as the x-coordinate of the original point.
C’(–4, –4) –5 –6
A’(–7, –6) –7