Splash Screen

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Splash Screen
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Lesson Menu
Five-Minute Check (over Lesson 93) NGSSS Then/Now
New Vocabulary Key Concept Glide
Reflection Example 1 Graph a Glide
Reflection Theorem 9.1 Composition of
Isometries Example 2 Graph Other Compositions
of Isometries Theorem 9.2 Reflections in
Parallel Lines Theorem 9.3 Reflections in
Intersecting Lines Example 3 Reflect a Figure
in Two Lines Example 4 Real-World Example
Describe Transformations Concept Summary
Compositions of Translations
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5-Minute Check 1
The coordinates of quadrilateral ABCD before and
after a rotation about the origin are shown in
the table. Find the angle of rotation.

1. A
2. B
3. C
4. D

A. 90 counterclockwise B. 90 clockwise C. 60
clockwise D. 45 clockwise
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5-Minute Check 2
The coordinates of triangle XYZ before and after
a rotation about the origin are shown in the
table. Find the angle of rotation.

1. A
2. B
3. C
4. D

A. 180 clockwise B. 270 clockwise C. 90
clockwise D. 90 counterclockwise
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5-Minute Check 3
Draw the image of ABCD under a 180 clockwise
rotation about the origin.

1. A
2. B
3. C
4. D

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5-Minute Check 4
The point (2, 4) was rotated about the origin so
that its new coordinates are (4, 2). What was
the angle of rotation?
A. 180 clockwise B. 120 counterclockwise C. 90
counterclockwise D. 60 counterclockwise

1. A
2. B
3. C
4. D

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NGSSS
MA.912.G.2.4 Apply transformations to polygons to
determine congruence, similarity, and symmetry.
Know that images formed by translations,
reflections, and rotations are congruent to the
original shape. Create and verify tessellations
of the plane using polygons. MA.912.G.2.6 Use
coordinate geometry to prove properties of
congruent, regular and similar polygons, and to
perform transformations in the plane.
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Then/Now
You drew reflections, translations, and
rotations. (Lessons 91, 92, and 93)

• Draw glide reflections and other compositions of
  isometries in the coordinate plane.

• Draw compositions of reflections in parallel and
  intersecting lines.

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Vocabulary

• composition of transformations
• glide reflection

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Concept
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Example 1
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.
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Example 1
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)
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Example 1
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
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Example 1
Quadrilateral RSTU has vertices R(1, 1), S(4,
2), T(3, 4), and U(1, 3). Graph RSTU and its
image after a translation along (4, 1) and a
reflection in the x-axis. Which point is located
at (3, 0)?
A. R' B. S' C. T' D. U'

1. A
2. B
3. C
4. D

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Concept
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Example 2
Graph Other Compositions of Isometries
?TUV has vertices T(2, 1), U(5, 2), and V(3,
4). Graph ?TUV and its image after a translation
along (1 , 5) and a rotation 180 about the
origin.
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Example 2
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)
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Example 2
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
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Example 2
?JKL has vertices J(2, 3), K(5, 2), and L(3, 0).
Graph ?TUV and its image after a translation
along (3, 1) and a rotation 180 about the
origin. What are the new coordinates of L''?
A. (3, 1) B. (6, 1) C. (1, 6) D. (1, 6)

1. A
2. B
3. C
4. D

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Concept
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Concept
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Example 3
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''.
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Example 3
Reflect a Figure in Two Lines
Step 1 Reflect EFGH in line p.
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Example 3
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.
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Example 3
Copy and reflect figure ABC in line S and then
line T. Then describe a single transformation
that maps ABC onto A''B''C''.
A. ABC is reflected across lines and translated
down 2 inches. B. ABC is translated down 2 inches
onto A''B''C''. C. ABC is translated down 2
inches and reflected across line t. D. ABC is
translated down 4 inches onto A''B''C''.

1. A
2. B
3. C
4. D

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Example 4
Describe Transformations
A. LANDSCAPING Describe the transformations that
are combined to create the brick pattern shown.
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Example 4
Describe Transformations
Step 1 A brick is copied and translated to the
right one brick length.
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Example 4
Describe Transformations
Step 2 The brick is then rotated
90counterclockwise about point M, given here.
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Example 4
Describe Transformations
Step 3 The new brick is in place.
Answer The pattern is created by successive
translations and rotations shown above.
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Example 4
Describe Transformations
B. LANDSCAPING Describe the transformations that
are combined to create the brick pattern shown.
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Example 4
Describe Transformations
Step 1 Two bricks are copied and translated 1
brick length to the right.
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Example 4
Describe Transformations
Step 2 The two bricks are then rotated 90?
clockwise or counterclockwise about point M,
given here.
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Example 4
Describe Transformations
Step 3 The new bricks are in place.
Another transformation is possible.
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Example 4
Describe Transformations
Step 1 Two bricks are copied and rotated 90?
clockwise about point M.
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Example 4
Describe Transformations
Step 2 The new bricks are in place.
Answer The pattern is created by successive
rotations of two bricks or by alternating
translations then rotations.
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Example 4
A. What transformation must occur to the brick at
point M to further complete the pattern shown
here?
A. The brick must be rotated 180
counterclockwise about point M. B. The brick must
be translated one brick width right of point
M. C. The brick must be rotated 90
counterclockwise about point M. D. The brick must
be rotated 360 counterclockwise about point M.

1. A
2. B
3. C
4. D

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Example 4
B. What transformation must occur to the brick at
point M to further complete the pattern shown
here?
A. The two bricks must be translated one brick
length to the right of point M. B. The two
bricks must be translated one brick length down
from point M. C. The two bricks must be rotated
180 counterclockwise about point M. D. The brick
must be rotated 90 counterclockwise about point
M.

1. A
2. B
3. C
4. D

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Concept
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End of the Lesson