1. Warm-Up
NO NOTES!
Despite the fact that you have not memorized the rules, determine what each of these transformations would do to an image. (reflect across y-axis, reflect across x-axis, reflect across y=x, rotate 90°, rotate 180°, rotate 270°)
(x,y)→(-x,y) 2. (x,y) →(-x,-y)
3. (x,y) →(-y,x) 4. (x,y) →(y,x)
5. (x,y) →(x,-y) 6. (x,y) →(y,-x)

2. Practice

3. Practice

4. More Practice!

5. Even More Practice!

6. Compositions of Transformations
When we apply one transformation to a figure, then we apply another transformation to its image, the resulting transformation is called a composition of two transformations.
In a figure, point A would transform from A to A’ to A”

7. Example

8. Now you try
Name the single translation that can replace the composition of these three translations:
(𝑥,𝑦)→(𝑥+2,𝑦+3)→(𝑥−5,𝑦+7)→(𝑥+13,𝑦)
2. Name the single rotation that can replace the composition of these three rotations about the same center of rotation: 45°, then 50 °, then 85 °.

9. Let’s do the exit ticket once more, but this time on a coordinate plane
Create any triangle you want, on a coordinate plane, with specific ordered pairs for the corners of the object.
Translate this triangle anywhere you want. Make sure you write the rule for this translation.
Rotate the new image 180° around the origin (0,0)
Reflect the newest image over the y-axis.

10. Puzzle!
Try to figure out what would come next in the series, and sketch the next two figures:

11. Mini-Review and Challenge
Draw a figure which contains reflectional symmetry but only 1 rotational symmetry
Draw a figure that has more than one rotational symmetry but no reflectional symmetry.

12. Puzzle!
List all of the letters in the alphabet, when they are capital letters, that have more than one rotational symmetry
List all of the letters in the alphabet, when they are capital letters, that have reflectional symmetry
List all of the letters that have neither!

13. Puzzle!
Is it possible for a triangle to have exactly one line of reflectional symmetry? Exactly 2? Exactly 3? More than 3?
Support your answers with sketches.

14. Puzzle! Draw two points on a piece of paper.
Connect the two points with a curve which would create a figure with more than one rotational symmetry and no reflectional symmetries.