2. Transparency 9 Click the mouse button or press the Space Bar to display the answers.

3. Splash Screen

4. Example 9-2b Objective Graph rotations on a coordinate plane

5. Example 9-2b Vocabulary Rotation A transformation involving the turning or spinning of a figure around a fixed point

6. Example 9-2b Vocabulary Center of rotation The fixed point a rotation of a figure turns or spins around

7. Example 9-2b Review Vocabulary Angle of rotation The degree measure of the angle through which a figure is rotated

8. Lesson 9 Contents Example 1Rotations in the Coordinate Plane Example 2Angle of Rotation

9. Example 9-1a Graph  QRS with vertices Q(1, 1), R(3, 4), and S(4, 1). Then graph the image of  QRS after a rotation of counterclockwise about the origin, and write the coordinates of its vertices. 1/2 Plot the 3 coordinates Q(1, 1) R(3, 4) S(4, 1) Label Q Label R Label S Q R S Connect the dots in order that was plotted Now the fun begins!

10. Example 9-1a Graph  QRS with vertices Q(1, 1), R(3, 4), and S(4, 1). Then graph the image of  QRS after a rotation of counterclockwise about the origin, and write the coordinates of its vertices. 1/2 Q R S 180 0 is half of a circle 180 0 is a straight line Let’s use the straight line definition of 180 0

11. Example 9-1a Graph  QRS with vertices Q(1, 1), R(3, 4), and S(4, 1). Then graph the image of  QRS after a rotation of counterclockwise about the origin, and write the coordinates of its vertices. 1/2 Q R S Since the rotation is 180 0 we will be plotting the image in the opposite quadrant as the original Begin with Q(1,1) and draw a straight line into the opposite quadrant by passing through the origin (0, 0) Label Q’ Q’

12. Example 9-1a Graph  QRS with vertices Q(1, 1), R(3, 4), and S(4, 1). Then graph the image of  QRS after a rotation of counterclockwise about the origin, and write the coordinates of its vertices. 1/2 Q R S Begin with R(3, 4) and draw a straight line into the opposite quadrant by passing through the origin (0, 0) Label R’ Q’ R’

13. Example 9-1a Graph  QRS with vertices Q(1, 1), R(3, 4), and S(4, 1). Then graph the image of  QRS after a rotation of counterclockwise about the origin, and write the coordinates of its vertices. 1/2 Q R S Begin with S(4,1) and draw a straight line into the opposite quadrant by passing through the origin (0, 0) Label S’ Q’ R’ S’ Connect the dots in order

14. Example 9-1a Graph  QRS with vertices Q(1, 1), R(3, 4), and S(4, 1). Then graph the image of  QRS after a rotation of counterclockwise about the origin, and write the coordinates of its vertices. 1/2 Q R S Q’ R’ S’ Q’(-1, -1) R’(-3, -4) S’(-4, -1) Note: Since plotted in opposite quadrant then the numbers are the same just opposite signs Answer: Must have the graph AND the coordinates

15. Example 9-1b Answer: A'(–4, –1), B'(–2, –1), C'(–2, –4) Graph with vertices A(4, 1), B(2, 1), and C(2, 4). Then graph the image of after a rotation of counterclockwise about the origin, and write the coordinates of its vertices. 1/2

16. Graph  XYZ with vertices X(2, 2), Y(4, 3), and Z(3, 0) Then graph the image of  XYZ after a rotation 90° counterclockwise about the origin. Write coordinates of each vertices Example 9-2a 2/2 Plot the 3 coordinates X(2, 2) Y(4, 3) Z(3, 0) Label X Label Y Label Z X Y Z Connect the dots in order that was plotted

17. Graph  XYZ with vertices X(2, 2), Y(4, 3), and Z(3, 0) Then graph the image of  XYZ after a rotation 90° counterclockwise about the origin. Write coordinates of each vertices Example 9-2a 2/2 X Y Z 90 0 is one fourth a circle 90 0 makes a right triangle Let’s use the right angle of 900 0

18. Graph  XYZ with vertices X(2, 2), Y(4, 3), and Z(3, 0) Then graph the image of  XYZ after a rotation 90° counterclockwise about the origin. Write coordinates of each vertices Example 9-2a 2/2 X Y Z Begin with X and draw a line to the origin Counterclockwise means to go to the left (From Quadrant 1 to Quadrant 2) From the origin make a right angle Label X’ X’

19. Graph  XYZ with vertices X(2, 2), Y(4, 3), and Z(3, 0) Then graph the image of  XYZ after a rotation 90° counterclockwise about the origin. Write coordinates of each vertices Example 9-2a 2/2 X Y Z Begin with Y and draw a line to the origin Counterclockwise means to go to the left (From Quadrant 1 to Quadrant 2) From the origin make a right angle Label Y’ X’ Y’

20. Graph  XYZ with vertices X(2, 2), Y(4, 3), and Z(3, 0) Then graph the image of  XYZ after a rotation 90° counterclockwise about the origin. Write coordinates of each vertices Example 9-2a 2/2 X Y Z Begin with Z and draw a line to the origin Counterclockwise means to go to the left (From Quadrant 1 to Quadrant 2) From the origin make a right angle Label Z’ X’ Y’ Z’

21. Graph  XYZ with vertices X(2, 2), Y(4, 3), and Z(3, 0) Then graph the image of  XYZ after a rotation 90° counterclockwise about the origin. Write coordinates of each vertices Example 9-2a 2/2 X Y Z X’ Y’ Z’ Connect the dots in order X’(-2, 2) Y’(-3, 4) Z’(0, 3) Answer: Must have the graph AND the coordinates

22. Example 9-1b 1/2 Graph  ABC with vertices A(1, 2), B(1, 4), and C(5, 5) Then graph the image of  ABC after a rotation 90° counterclockwise about the origin. Write coordinates of each vertices A B C A’B’ C’ A’(-2, 1) B’(-4, 1) C’(-5, 5) Answer:

23. End of Lesson 9 Assignment Lesson 6:9Rotations3 - 12 All

24. QUILTS Copy and complete the quilt piece shown below so that the completed figure has rotational symmetry with 90°, 180°, and 270°, as its angles of rotation. Example 9-2a 1 st copy the pattern

25. Example 9-2a Rotate the figure 90 , 180 , and 270  counterclockwise. Use a 90  rotation clockwise to produce the same rotation as a 270  rotation counterclockwise. 90° counterclockwise

26. Example 9-2a Rotate the figure 90 , 180 , and 270  counterclockwise. Use a 90  rotation clockwise to produce the same rotation as a 270  rotation counterclockwise. 180° counterclockwise 90° counterclockwise

27. Example 9-2a Answer: 270° counterclockwise 180° counterclockwise

28. Example 9-2b QUILTS Copy and complete the quilt piece shown below so that the completed figure has rotational symmetry with 90°, 180°, and 270°, as its angles of rotation. *

29. Example 9-2b Answer: