1. 4.4 Transformations with Matrices
2. Reflections and Rotations

2. 2) Reflections
A reflection, or flip, is a transformation that creates symmetry. 
You can use matrix multiplication to graph reflections in the coordinate plane.
There are four reflection matrices you are responsible for knowing.

3. 2) Reflections
Reflection in the y-axis Reflection in the x-axis

4. 2) Reflections
Reflection in the line y = x Reflection in the line y = -x

5. 2) Reflections
Example 1:  Given triangle ABC with A (–4, 1), B (– 2, 5) and C (0, 2), reflect the triangle across the y-axis. Then, sketch the image.
A B C

6. 2) Reflections
Example 1:  Given triangle ABC with A (–4, 1), B (– 2, 5) and C (0, 2), reflect the triangle across the y-axis. Then, sketch the image.
A B C
y-axis reflection matrix

7. 2) Reflections
Example 1:  Given triangle ABC with A (–4, 1), B (– 2, 5) and C (0, 2), reflect the triangle across the y-axis. Then, sketch the image.
A B C
A’ B’ C’
y-axis reflection matrix

8. 2) Reflections

9. 2) Reflections
Example 2: Given triangle ABC where A (–4, 1), B (– 2, 5) and C (0, 2), reflect the triangle across the x-axis. Then, sketch the image.

10. 2) Reflections
Example 2: Given triangle ABC where A (–4, 1), B (– 2, 5) and C (0, 2), reflect the triangle across the x-axis. Then, sketch the image.
A B C

11. 2) Reflections
Example 2: Given triangle ABC where A (–4, 1), B (– 2, 5) and C (0, 2), reflect the triangle across the x-axis. Then, sketch the image.
A B C
x-axis reflection matrix

12. 2) Reflections
Example 2: Given triangle ABC where A (–4, 1), B (– 2, 5) and C (0, 2), reflect the triangle across the x-axis. Then, sketch the image.
A’ B’ C’
A B C
x-axis reflection matrix

13. 2) Reflections

14. 2) Rotations
A rotation is a transformation that turns a figure about a fixed point called a center of rotation. 
You can rotate a figure as much as 360o. 
In this text, all rotations are counterclockwise about the origin.

15. 2) Rotations Rotation of 90o Rotation of 360o

16. 2) Rotations
Example 1:  Given triangle ABC where A (–4, 1), B (– 2, 5) and C (0, 2), rotate the triangle 270°.  Then, sketch the image. 

17. 2) Rotations
Example 1:  Given triangle ABC where A (–4, 1), B (– 2, 5) and C (0, 2), rotate the triangle 270°.  Then, sketch the image. 
A B C

18. 2) Rotations
Example 1:  Given triangle ABC where A (–4, 1), B (– 2, 5) and C (0, 2), rotate the triangle 270°.  Then, sketch the image. 
A B C
270o rotation matrtix

19. 2) Rotations
Example 1:  Given triangle ABC where A (–4, 1), B (– 2, 5) and C (0, 2), rotate the triangle 270°.  Then, sketch the image. 
A B C
A’ B’ C’
270o rotation matrtix

20. 2) Rotations

21. 2) Rotations
Example 2:  The matrix below represents the vertices of a polygon. Write a matrix to represent the vertices after a rotation of 90o.
A B C D

22. 2) Rotations
Example 2:  The matrix below represents the vertices of a polygon. Write a matrix to represent the vertices after a rotation of 90o.
A B C D
90o rotation matrtix

23. 2) Rotations
Example 2:  The matrix below represents the vertices of a polygon. Write a matrix to represent the vertices after a rotation of 90o.
A B C D
A’ B’ C’ D’
90o rotation matrtix

24. Homework
Create some way to remember the 8 matrices used for reflections and rotations.
You are responsible for knowing all 8.
The matrices are located on p.193 and p.194
2) p.196 #10, 11, 13, 14, 18-21, 31, 32
3) QUIZ WEDNESDAY – section 4.4