1. composition of transformations glide reflection
Vocabulary

2. Concept

3. Graph a Glide Reflection
Quadrilateral BGTS has vertices B(–3, 4), G(–1, 3), T(–1 , 1), and S(–4, 2). Graph BGTS and its image after a translation along 5, 0 and a reflection in the x-axis.
Example 1

4. Step 1 translation along 5, 0 (x, y) → (x + 5, y)
Graph a Glide Reflection
Step 1 translation along 5, 0
(x, y) → (x + 5, y)
B(–3, 4) → B'(2, 4)
G(–1, 3) → G'(4, 3)
S(–4, 2) → S'(1, 2)
T(–1, 1) → T'(4, 1)
Example 1

5. Step 2 reflection in the x-axis (x, y) → (x, –y) B'(2, 4) → B''(2, –4)
Graph a Glide Reflection
Step 2 reflection in the x-axis
(x, y) → (x, –y)
B'(2, 4) → B''(2, –4)
G'(4, 3) → G''(4, –3)
S'(1, 2) → S''(1, –2)
T'(4, 1) → T''(4, –1)
Answer:
Example 1

6. Concept

7. Graph Other Compositions of Isometries
ΔTUV has vertices T(2, –1), U(5, –2), and V(3, –4). Graph ΔTUV and its image after a translation along –1 , 5 and a rotation 180° about the origin.
Example 2

8. Step 1 translation along –1 , 5 (x, y) → (x + (–1), y + 5)
Graph Other Compositions of Isometries
Step 1 translation along –1 , 5
(x, y) → (x + (–1), y + 5)
T(2, –1) → T'(1, 4)
U(5, –2) → U'(4, 3)
V(3, –4) → V'(2, 1)
Example 2

9. Step 2 rotation 180 about the origin (x, y) → (–x, –y)
Graph Other Compositions of Isometries
Step 2 rotation 180 about the origin
(x, y) → (–x, –y)
T'(1, 4) → T''(–1, –4)
U'(4, 3) → U''(–4, –3)
V'(2, 1) → V''(–2, –1)
Answer:
Example 2

10. GSP Demo…

11. Concept

12. Concept

13. Reflect a Figure in Two Lines
Copy and reflect figure EFGH in line p and then line q. Then describe a single transformation that maps EFGH onto E''F''G''H''.
Example 3

14. Step 1 Reflect EFGH in line p.
Reflect a Figure in Two Lines
Step 1 Reflect EFGH in line p.
Example 3

15. Step 2 Reflect E'F'G'H' in line q.
Reflect a Figure in Two Lines
Step 2 Reflect E'F'G'H' in line q.
Answer: EFGH is transformed onto E''F''G''H'' by a translation down a distance that is twice the distance between lines p and q.
Example 3

16. Concept