1. 9.5 & 9.6 – Compositions of Transformations & Symmetry

2. Glide Reflection:
A transformation with a translation and then a reflection in a line parallel to the direction of the translation k Q P

3. Composition of Transformations:
Any two transformations combined to form a single transformation

4. If lines k and m are parallel, then a reflection in line k followed by a reflection in line m is a
___________. If ____ is the image of P after the two reflections, then:
translation

5. If lines k and m intersect at point P, then a reflection in k followed by a reflection in m is a
_________. If ____ is the image of P after the two reflections, then:
rotation
The angle of rotation is 2x°, where x° is the measure of the acute or right angle formed by k and m

6. A 1. Translation: (x, y) → (x + 2, y) Reflection: in the x-axis
Graph the image of A(1, –2) after the described glide reflection.
1. Translation: (x, y) → (x + 2, y)
Reflection: in the x-axis A

7. A 2. Translation: (x, y) → (x – 1, y + 3) Reflection: in x = 2
Graph the image of A(1, –2) after the described glide reflection.
2. Translation: (x, y) → (x – 1, y + 3)
Reflection: in x = 2 A

8. The vertices of ABC are A(3, 1), B(1, 5) and C(5, 3)
The vertices of ABC are A(3, 1), B(1, 5) and C(5, 3). Graph the image of ABC after a composition of the transformations in the order they are listed.
Reflection: y-axis
Translation: (x, y) → (x + 3, y – 5) B C A

9. (x, y) → (y, x) B (3, 1) (1, 3) C (1, –3) A (–3, 1) (5, –1) (–1, 5)
The vertices of ABC are A(3, 1), B(1, 5) and C(5, 3). Graph the image of ABC after a composition of the transformations in the order they are listed.
Reflection: y = 1
Reflection: y = x
(x, y) →
(y, x) B
(3, 1)
(1, 3) C
(1, –3) A
(–3, 1)
(5, –1)
(–1, 5)

10. Describe the composition of transformations.
Reflection:
x-axis
Translation:
(x, y) → (x + 6, y + 2)

11. Describe the composition of transformations.
Rotation:
90°
Reflection:
x-axis

12. In the diagram, is reflected in line r, and
is reflected in line s.
7. A translation maps onto which segment?

13. In the diagram, is reflected in line r, and
is reflected in line s.
8. Which lines are perpendicular to
r and s

14. In the diagram, is reflected in line r, and
is reflected in line s.
9. Name a segment parallel to

15. In the diagram, is reflected in line r, and
is reflected in line s.
10. If the distance between r and s is 2.4 inches, what is the length of
2.4  2
4.8 inches

16. In the diagram, is reflected in line r, and
is reflected in line s.
11. Is the distance from to r the same as the distance from C to r?
Yes,
Def. of Reflection

17. 12. Find the angle of rotation that maps T onto
75  2
150°

18. 13. Find the angle of rotation that maps A onto
99  2
198°

19. Line of Symmetry:
The figure can be mapped onto itself by a reflection in the line
Rotational Symmetry:
The figure can be mapped onto itself by a rotation of 180° or less around a point

20. Rotational: _________
Identify the number of line and rotational symmetry of the figure shown. 1
Line: _____________
Rotational: _________
none

21. Rotational: _________
Identify the number of line and rotational symmetry of the figure shown.
none
Line: _____________
Rotational: _________
none

22. Rotational: _________
Identify the number of line and rotational symmetry of the figure shown.
360 3 =
120° 3
Line: _____________
Rotational: _________
120°

23. Rotational: _________
Identify the number of line and rotational symmetry of the figure shown.
360 4 =
90° 4
Line: _____________
Rotational: _________
90°,
180°

24. Rotational: ____________
Identify the number of line and rotational symmetry of the figure shown.
360 6 =
60° 6
Line: _____________
Rotational: ____________
60°,
120°,
180°

25. Rotational: _________
Identify the number of line and rotational symmetry of the figure shown. 1
Line: _____________
Rotational: _________
none

26. Rotational: _________
Identify the number of line and rotational symmetry of the figure shown.
360 4 =
90° 4
Line: _____________
Rotational: _________
90°,
180°

27. Rotational: _________
Identify the number of line and rotational symmetry of the figure shown. 1
Line: _____________
Rotational: _________
none

28. Rotational: _________
Identify the number of line and rotational symmetry of the figure shown.
360 2 =
180°
Line: _____________
Rotational: _________ 2
180°

29. HW Problems 9.5 #13 Translation: Rotation: 180°
9.6
3, 6, 9, 11, all
3, 4, 6, 7, 9, 11, 12
9.5 #13
Translation:
(x, y) → (x + 5, y + 1)
Rotation:
180°