1. Name the reflected image of BC in line m.
Starter(s)
Name the reflected image of BC in line m.
___ A. B. C. D.
5-Minute Check 1

2. Name the reflected image of AB in line m.
___ A. B. C. D.
5-Minute Check 2

3. Name the reflected image of ΔAGB in line m.
A. ΔFGE
B. ΔEGD
C. ΔCGD
D. ΔBCG
5-Minute Check 3

4. Name the reflected image of B in line m.
A. D
B. E
C. F
D. G
5-Minute Check 4

5. Name the reflected image of ABCF in line m.
A. AFEB
B. DCBE
C. EDCF
D. FEDA
5-Minute Check 5

6. Which of the following shows a reflection in the x-axis?
A. B.
C. D.
5-Minute Check 6

7. You found the magnitude and direction of vectors.
9.2 Translations
You found the magnitude and direction of vectors.
Draw translations.
Draw translations in the coordinate plane.
Then/Now

8. translation vector
Vocabulary

9. Concept

10. Concept

11. Example 1) Translations in the Coordinate Plane
A. Graph ΔTUV with vertices T(–1, –4), U(6, 2), and V(5, –5) along the vector –3, 2.
Example 2

12. The vector indicates a translation 3 units left and 2 units up.
Example 1) Translations in the Coordinate Plane
The vector indicates a translation 3 units left and 2 units up.
(x, y) → (x – 3, y + 2)
T(–1, –4) → T’(–4, –2)
U(6, 2) → U’(3, 4)
V(5, –5) → V’(2, –3)
Answer:
Example 2

13. Example 1) Translations in the Coordinate Plane
B. Graph pentagon PENTA with vertices P(1, 0), E(2, 2), N(4, 1), T(4, –1), and A(2, –2) along the vector –5, –1.
Example 2

14. The vector indicates a translation 5 units left and 1 unit down.
Example 1) Translations in the Coordinate Plane
The vector indicates a translation 5 units left and 1 unit down.
(x, y) → (x – 5, y – 1)
P(1, 0) → P’(–4, –1)
E(2, 2) → E’(–3, 1)
N(4, 1) → N’(–1, 0)
T(4, –1) → T’(–1, –2)
A(2, –2) → A’(–3, –3)
Answer:
Example 2

15. 1)
A. Graph ΔABC with the vertices A(–3, –2), B(4, 4), C(3, –3) along the vector –1, 3. Choose the correct coordinates for ΔA'B'C'.
A. A'(–2, –5), B'(5, 1), C'(4, –6)
B. A'(–4, –2), B'(3, 4), C'(2, –3)
C. A'(3, 1), B'(–4, 7), C'(1, 0)
D. A'(–4, 1), B'(3, 7), C'(2, 0)
Example 2

16. 1)
B. Graph ΔGHJK with the vertices G(–4, –2), H(–4, 3), J(1, 3), K(1, –2) along the vector 2, –2. Choose the correct coordinates for ΔG'H'J'K'.
A. G'(–6, –4), H'(–6, 1), J'(1, 1), K'(1, –4)
B. G'(–2, –4), H'(–2, 1), J'(3, 1), K'(3, –4)
C. G'(–2, 0), H'(–2, 5), J'(3, 5), K'(3, 0)
D. G'(–8, 4), H'(–8, –6), J'(2, –6), K'(2, 4)
Example 2

17. Example 2) Describing Translations
A. ANIMATION The graph shows repeated translations that result in the animation of the raindrop. Describe the translation of the raindrop from position 2 to position 3 in function notation and in words.
Example 3

18. Answer: function notation: (x, y) → (x – 2, y – 3)
Example 2) Describing Translations
The raindrop in position 2 is (1, 2). In position 3, this point moves to (–1, –1). Use the translation function (x, y) → (x + a, y + b) to write and solve equations to find a and b.
(1 + a, 2 + b) or (–1, –1)
1 + a = – b = –1
a = – b = –3
Answer: function notation: (x, y) → (x – 2, y – 3)
So, the raindrop is translated 2 units left and 3 units down from position 2 to 3.
Example 3

19. Answer: translation vector:
Example 2) Describing Translations
B. ANIMATION The graph shows repeated translations that result in the animation of the raindrop. Describe the translation of the raindrop from position 3 to position 4 using a translation vector.
(–1 + a, –1 + b) or (–1, –4)
–1 + a = –1 –1 + b = –4
a = 0 b = –3
Answer: translation vector:
Example 3

20. 2)
A. The graph shows repeated translations that result in the animation of the soccer ball. Choose the correct translation of the soccer ball from position 2 to position 3 in function notation.
A. (x, y) → (x + 3, y + 2)
B. (x, y) → (x + (–3), y + (–2))
C. (x, y) → (x + (–3), y + 2)
D. (x, y) → (x + 3, y + (–2))
Example 3

21. 2)
B. The graph shows repeated translations that result in the animation of the soccer ball. Describe the translation of the soccer ball from position 3 to position 4 using a translation vector.
A. –2, –2
B. –2, 2
C. 2, –2
D. 2, 2
Example 3