1. Translations
Translations
Chapter 9.2
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2. Draw translated images using coordinates. translation composition
Draw translated images by using repeated reflections.
Standard Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections. (Key)
Lesson 2 MI/Vocab

3. Translation
A transformation that maps every two points P and Q to points P’ and Q’, so that the following properties are true:
PP’ = QQ’
PP’ // QQ’, or PP’ and QQ’ are collinear
Is a composite of two reflections over // lines

4. Translations in the Coordinate Plane
Triangle TUV has vertices T(–1, –4), U(6, 2), and V(5, –5). If ΔTUV is translated 3 units up and 5 units left to create ΔT'U'V', what are the coordinates of the vertices of ΔT'U'V'?
Lesson 2 Ex1

5. Plot points T(–1, –4), U(6, 2), and V(5, –5).
Do not translate the triangle!!!
Translate the vertices 3 units up and 5 units left.
Then connect the dots to create ΔT'U'V',
T’: (-6, -1) U’
U’: (1, 5) U
V’: (0, -2) V’ T’ T V

6. Solve the Item (quicker with math!)
Translations in the Coordinate Plane
Solve the Item (quicker with math!)
“Three units up” 
y + 3
“Five units left” 
x – 5
(x, y)  (x – 5, y + 3).
T(–1, –4) T' (–1 – 5, –4 + 3) or T' (–6, –1)
U(6, 2)  U' (6 – 5, 2 + 3) or U' (1, 5)
V(5, –5)  V' (5 – 5, –5 + 3) or V' (0, –2)
Lesson 2 Ex1

7. Translations in the Coordinate Plane
Triangle ABC has vertices A(-2, 3), B(4, -1), and C(-5, -3). If ΔABC is translated 4 units down and 3 units right to create ΔA'B'C', what are the coordinates of the vertices of ΔA'B'C'?
A'(1, -1), B'(7, -5), C'(-1, -7)
Lesson 2 Ex1

8. COORDINATE GEOMETRY Parallelogram LMNP has vertices L(–1, 2), M(1, 4), N(3, 2), and P(1, 0). Graph LMNP and its image for the translation (x, y)  (x + 3, y – 4).
A. B.
C. D. A B C D
Lesson 2 CYP1

9. Repeated Translations
ANIMATION The graph shows repeated translations that result in the animation of a raindrop.
Find the translation that moves raindrop 2 to raindrop 3.
x – 2
y – 3
The translation from raindrop 2 to raindrop 3 is (x – 2, y – 3)
Lesson 2 Ex2

10. The translation from raindrop 3 to raindrop 4 is (x, y – 3)
Repeated Translations
ANIMATION The graph shows repeated translations that result in the animation of a raindrop.
Find the translation that moves raindrop 3 to raindrop 4.
x + 0
y - 3
The translation from raindrop 3 to raindrop 4 is (x, y – 3)
Lesson 2 Ex2

11. A. (x + 3, y + 1) B. (x – 3, y – 1) C. (x + 3, y – 1)
A. ANIMATION The graph shows repeated translations that result in the animation of a lightning bolt. Find the translation that moves lightning bolt 3 to lightning bolt 4.
A. (x + 3, y + 1)
B. (x – 3, y – 1)
C. (x + 3, y – 1)
D. (x – 3, y + 1) A B C D
Lesson 2 CYP2

12. A. (x + 2, y + 2) B. (x – 2, y – 2) C. (x + 2, y – 2)
B. ANIMATION The graph shows repeated translations that result in the animation of a lightning bolt. Find the translation that moves lightning bolt 2 to lightning bolt 1.
A. (x + 2, y + 2)
B. (x – 2, y – 2)
C. (x + 2, y – 2)
D. (x – 2, y + 2) A B C D
Lesson 2 CYP2

13. In the figure, lines p and q are parallel.
Find a Translation Using Reflections
In the figure, lines p and q are parallel.
Determine whether the red figure is a translation image of the blue preimage, quadrilateral EFGH.
Answer:
Quadrilateral E''F''G''H'' is not a translation image of quadrilateral EFGH.
Lesson 2 Ex3

14. In the figure, lines n and m are parallel
In the figure, lines n and m are parallel. Determine whether ΔA''B''C'' is a translation image of the preimage, ΔABC.
A. yes
B. no
C. cannot be determined A B C
Lesson 2 CYP3

15. Chapter 9-2 Pg 506 2 – 10 even, 12 – 17 all, 24, 26, and 39
Homework
Chapter 9-2
Pg 506
2 – 10 even, 12 – 17 all, 24, 26, and 39