Lesson 7.1 • Transformations and Symmetry
Name
Period
Date
In Exercises 1–3, perform each transformation.
1. Reflect !TRI across line !.
2. Rotate PARL 270° clockwise
3. Translate PENTA by
about Q.
the given vector.
I
L
T
T
R
P
R
Q
!
N
A
A
P E
4. ABCDE and its reflected image, A!B!C!D!E!, are shown below.
Use construction tools to locate the line of reflection, !. Explain
your method.
D
D!
E!
C!
C
E
B
A!
B!
A
In Exercises 5–8, identify the type(s) of symmetry in each figure.
5. Equilateral triangle
6. Rectangle
7. Isosceles triangle
8. Square
In Exercises 9–12, draw each polygon and identify the type(s) of symmetry
in each. Draw all lines of reflection and mark centers of rotation.
9. Rhombus
10. Parallelogram
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11. Isosceles trapezoid
12. Square
CHAPTER 7
47
Lesson 7.2 • Properties of Isometries
Name
Period
Date
In Exercises 1–3, draw the image according to the rule and identify the
type of transformation.
1. (x, y) → ("x, "y)
2. (x, y) → (x " 4, y # 6)
3. (x, y) → (4 " x, y)
y
y
6
y
8
6
4
2
–6
–4 –2
4
4
2
4
6
–2
2
x
–8
4
–4
–4
x
4
6
x
–2
–4
–6
2
–2
–4
–4
In Exercises 4 and 5, the Harbour High Geometry Class is holding a Fence
Race. Contestants must touch each fence at some point as they run from
S to F. Use your geometry tools to draw the shortest possible race path.
5.
Fence 1
4.
Fence
S
S
F
Fence 2
F
In Exercises 6–8, complete the ordered pair rule that transforms
each triangle to its image. Identify the transformation. Find all
missing coordinates.
6. (x, y) → (_____, _____)
7. (x, y) → (_____, _____)
y
8. (x, y) → (_____, _____)
y
y
B!
R
B(–5, 2)
(5, 2)
C!
T (0, 7)
R!(4, 5)
A!(8, 2)
x
R
S(3, 3)
S!
x
C
48
A(–5, –4)
CHAPTER 7
Q(–2, 1) Q!(2, 1)
P(–7, –3)
R!(3, 0)
T!
x
P!
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Lesson 7.3 • Compositions of Transformations
Name
Period
Date
In Exercises 1–8, name the single transformation that can replace the
composition of each set of multiple transformations.
1. Translation by !#4, #1", followed by !#2, "3", followed by
!"8, #7"
2. Rotation 60° clockwise, followed by 80° counterclockwise, followed
by 25° counterclockwise all about the same center of rotation
3. Reflection across vertical line m, followed by reflection across vertical
line n, where n is 8 units to the right of m
4. Reflection across vertical line p, followed by reflection across horizontal
line q
5. Reflection across vertical line n, followed by reflection across vertical
line m, where n is 8 units to the right of m
6. Reflection across horizontal line q, followed by reflection across vertical
line p
7. Translation by !#6, 0", followed by reflection across the y-axis
8. Reflection across the y-axis, followed by translation by !#6, 0"
In Exercises 9–11, copy the figure onto your paper and use your
geometry tools to perform the given transformation.
R
!", and P$, the reflected image
9. Locate P!, the reflected image across OR
!". Find m"ROT and give a single transformation that
of P!across OT
maps P to P$.
P
O
T
10. Locate P!, the reflected image across k, and P$, the reflected image
k
of P!across !. Find the distance between ! and k and give a single
transformation that maps P to P$.
11. Draw five glide-reflected images of the triangle.
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©2008 Key Curriculum Press
!
P
CHAPTER 7
49