12.1.4 Compositions of Transformations - Worksheet
Example 1: Draw the result of each composition of isometries. 1. Translate △ DEF along u and then reflect it across line l .
2. Reflect rectangle PQRS across line m and then translate it along v .
u ⇀
v ⇀
F
Q
R
m
D
E
l
P
S
3. △ ABC has vertices A (1, − l), B (4, − l), and C (3, 2). Reflect △ ABC across the y -axis and then translate it along the vector 〈 0, − 2 〉 .
Example 2: 4. To create the opening graphics for a televised football game, an animator reflects a picture of a football helmet across line l . She then reflects its image across line m , which intersects line l at a 50° angle. Describe a single transformation that moves the helmet from its starting position to its final position.
l
m
50°
Example 3: Copy each figure and draw two lines of reflection that produce an equivalent transformation. 5. translation: △ EFG → △ EFG′ E 6. rotation with center P : △ ABC → △ A′B ′ C B’ C’
E
E’
E’
C
A’
F
F
G’
G’
F’
F’
G
G
A
P
B
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