1. 12.1 – Reflections 12.5 – Symmetry M217 – Geometry

2. ISOMETRY A movement or “translation” of a figure that preserves its original dimensions.  Reflections  Translations  Rotations

3. C C Reflection – A transformation that uses a line that acts like a mirror. Reflection Line of Reflection

4. Reflection Properties: Over y-axis (x, y) → ( ) A (-2, 4) B (2, -1) C (0, 4) D (-3, 0)

5. Reflection Properties: Over x-axis (x, y) → ( ) A (-2, 4) B (2, -1) C (0, 4) D (-3, 0)

6. Reflection Properties: Over y=x (x, y) → ( ) A (3, 4) B (1, 1) C (-3, 2) D (-32, 11) y = x

7. Ex: Reflection in the line y=1 y = 1 A (-1, 3) B (3, -2) C (0, 1) D (-2, 0)

8. Ex: Reflection in the line x = -2 x = -2 Triangle ABC: A (-1, 3)B (-3, -2)C (-4, 1)

9. The Line of Symmetry is the imaginary line where you could fold an image and have both halves match exactly.

12. Determine the number of lines of symmetry in each logo 1. 2. 3. 4. 5.

13. None – Go Hawks!!! Back

14. One – Go Bulls!!! Back

15. Almost one… Go Bears!!! Back

16. How many does the Mercedes logo have?

17. How many does the Star of David have?

18. Rotational Symmetry : if a figure can be mapped onto itself by a rotation of 180 o or less

19. rotational symmetry : if a figure can be mapped onto itself by a rotation of 180 o or less

20. rotational symmetry : if a figure can be mapped onto itself by a rotation of 180 o or less

21. rotational symmetry : if a figure can be mapped onto itself by a rotation of 180 o or less

22. Do You Get It? Is this a reflection? How many lines of symmetry? Does it have rotational symmetry? A A’ B B’ C C’

23. Do You Get It? If point R (-4,-5) is reflected over the y-axis, what are the coordinates of R’? If point S (0, 2) is reflected over the line x = -5, what are the coordinates of S’? Given points T ( -4, 3) and T’ ( -4, -2), what is the line of reflection?