GEOMETRY
CHAPTER 9 WORKBOOK
Reflection
Translation
Rotation
Dilation
SPRING 2017
0
1
Reflection
Reflection in the x-axis
Translations
Reflection in the y-axis
Reflection in the line y=x
Translation in the Coordinate Plane
Rotation
90°
180°
270°
Compositions of
Transformations
Glide reflection
Translation
Rotation
2
Symmetry
Line Symmetry
Dilation
Dilations in the Coordinate
Plane
Rotational Symmetry
Three – Dimensional
3
Geometry
Section 9.1 Notes: Reflections
Date:
1. I can draw reflections in the coordinate plane.
Learning Targets:
Vocab. and Topics
Definitions, Examples and Pictures
If the images to the
right describe a
reflection, in your
own words, define
reflection:
Line of Reflection
Reflection in a line
Draw the reflected image of quadrilateral WXYZ in line p.
Example 1
4
Quadrilateral JKLM has vertices J(2, 3), K(3, 2), L(2, –1), and M(0, 1).
Example 2
a) Graph JKLM and its image over x = 1.
b) Graph JKLM and its image over y = –2 .
Reflection in the x-axis
Reflections on a
Coordinate Plane
(𝒙, 𝒚) → (
Reflection in the y-axis
,
)
(𝒙, 𝒚) → (
,
)
5
Quadrilateral ABCD has vertices A(1, 1), B(3, 2), C(4, –1), and D(2, –3).
a) Graph the image reflected in the x – axis.
Example 3
b) Graph the image reflected in the y – axis.
Reflection in the
line 𝒚 = 𝒙
(𝒙, 𝒚) → (
,
)
Quadrilateral ABCD has vertices A(1, 1), B(3, 2), C(4, –1), and D(2, –3). Graph the image under reflection
of the line y = x.
Example 4
6
1. Graph the image of the figure below using the transformation given.
You Try!
a) Reflection across the x-axis
b) reflection across y = 3
2. Given the coordiante points of an image, graph the points below. Then use the transformaiton given to
plot the new figure.
c) reflection across the x-axis
d) reflection across y = −2
T(2, 2), C(2, 5), Z(5, 4), F(5, 0)
H(−1, −5), M(−1, −4), B(1, −2), C(3, −3)
Reflection over x-axis
Reflection over y-axis
Reflection over 𝒚 = 𝒙
Summary
7
9-1 Reflections
Exercises
Graph △FGH and its image in the given line.
1. x = –1
2. y = 1
Graph quadrilateral ABCD and its image in the given line.
3. x = 0
4. y = 1
Graph each figure and its image under the given reflection.
5. △DEF with D(–2, –1), E(–1, 3),
F(3, –1) in the x-axis
6. ABCD with A(1, 4), B(3, 2), C(2, –2),
D(–3, 1) in the y-axis
8
9
Geometry
Section 9.2 Notes: Translations
Date:
1. I can draw translations in the coordinate plane.
Learning Targets:
If the images to the
right describe a
translation, in
your own words,
define translation:
Translation
Translation Vector
Component Form
Translation on a
Coordinate Plane
10
a) Graph ∆TUV with vertices T(–1, –4), U(6, 2), and V(5, –5) along the vector −3, 2 .
Example 1
Example 1
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
The graph shows repeated translations that result in the animation of the raindrop.
a) Describe the translation of the raindrop from position 2 to position 3 in function notation and in words.
b) Describe the translation of the raindrop from position 3 to position 4 using a translation vector.
11
Example 3:
Given the rule,
(x, y )  (x − 2, y + 5) , describe in component form. Then transform the figure given
the vector.
You Try!
Example 4:
Use the translation (x, y) → ⟨−𝟓,𝟖⟩.
2. What is the image of
3. What is the preimage of F ’(23,
4. What is the preimage of
H ’(7, 25) ?
6. What is the preimage of
K ’(24,6) ?
1. What is the image of
B ( 4, 2 ) ?
5. What is the image of J
( 0, 2 ) ?
24) ?
D(21,5) ?
12
13
9-2 Translation
Graph each figure and its image along the given vector.
1. quadrilateral TUVW with vertices T(–3, –8), U(–6, 3), V(0, 3), and W(3, 0); 〈4, 5〉
2. △QRS with vertices Q(2, 5), R(7, 1), and S(–1, 2); 〈–1, –2〉
3. parallelogram ABCD with vertices A(1, 6), B(4, 5), C(1, –1), and D(–2, 0); 〈3, –2〉
14
4. Rectangle RECT has vertices R(–2, –1), E(–2, 2), C(3, 2), and T(3, –1).
Graph the figure and its image along the vector 〈2, –1〉.
15
Geometry
Section 9.3 Notes: Rotations
Date:
1. I can draw rotations in the coordinate plane.
Learning Targets:
If the images to the
right describe a
Rotation, in your
own words, define
rotation:
Center of Rotation
Angle of Rotation
Direction of
Rotation
90˚ Rotation
180˚ Rotation
270˚ Rotation
(𝒙, 𝒚) → (
(𝒙, 𝒚) → (
(𝒙, 𝒚) → (
, )
, )
, )
Rotations on a
Coordinate Plane
Describe in your
own words, how
will you help
yourself remember
this?
16
Example 1
Triangle DEF has vertices D(–2, –1), E(–1, 1), and F(1, –1). Graph ΔDEF and its image after a rotation of
270˚ about the origin?
Example 2
Hexagon DGJTSR is shown below. What is the image of point T after a 90° counterclockwise rotation
about the origin?
Example 3
Triangle PQR is shown below. What is the image of point Q after a 180° counterclockwise rotation about
the origin?
17
Example 4:
Find the image that represents the rotation of the polygon about the origin. Then graph the
polygon and its image.
A (1, −2 )
a) Rotate B ( 4, −1)
90°
C ( 3, −4 )
Find the image that represents the rotation of the polygon about the origin. Then graph the
polygon and its image.
A ( −1, −2 )
b) Rotate
B ( 2,1)
270°
C ( 3, −1)
D (1, −3)
18
19
9-3 Rotations
Graph each figure and its image after the specified rotation about the origin.
1. trapezoid FGHI has vertices F(7, 7),
G(9, 2), H(3, 2), and I(5, 7); 90°
2. △LMN has vertices L(–1, –1),
M(0, –4), and N(–6, –2); 90°
3. △ABC has vertices A(–3, 5), B(0, 2),
and C(–5, 1); 180°
4. parallelogram PQRS has vertices P(4, 7),
Q(6, 6), R(3, –2), and S(1, –1); 270°
20
5. Parallelogram WXYZ has vertices W(–2, 4), X(3, 6), Y(5, 2), and Z(0, 0).
Graph parallelogram WXYZ and its image after a rotation of 270° about the origin.
21
Geometry
Section 9.4 Notes: Compositions of Transformations
Date:
1. I can draw glide reflections and other compositions of isometries in the coordinate plane.
Learning Targets:
If the images to the
right describe a
composition of
transformations,
in your own
words, define
composition of
transformations:
Composition of
Transformations
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.
Example 1
22
Composition of
Isometries
(Transformations)
Example 2
Example 3
Example 4
ΔTUV has vertices T(2, –1), U(5, –2), and V(3, –4). Graph ΔTUV and its image after a translation along
〈–1 , 5〉 and a rotation 180° about the origin.
If PQRS is translated along < 3, −2 >, and reflected in 𝑦 = −1about the origin, what are the
coordinates of P’’Q’’R’’S’’? If P(3,2), Q(4,1), R(-1,2) and S(3,4).
Quadrilateral ABCD with A(1, 5), B(6, 2), C(-1, 3), D(-4, -2) is reflected in the line y = x and
then rotated 90°. Find the coordinates of the image.
23
Reflections in
Parallel Lines
Reflections in
Intersecting Lines
Example 6
A triangle is reflected in two parallel lines. The composition of the reflection produces a
translation 22 centimeters to the right. How far apart are the parallel lines?
24
25
9-4 Glide Reflections
Triangle XYZ has vertices X(6, 5), Y(7, –4) and Z(5, –5). Graph △XYZ and
its image after the indicated glide reflection.
1. Translation: along 〈1, 2〉
Reflection: in y–axis
2. Translation: along 〈2, 0〉
Reflection: in x = y
3. Translation: along 〈–3, 4〉
Reflection: in x–axis
26
4. Translation: along 〈–1, 3〉
Reflection: in x–axis
5.Triangle ABC has vertices A(3, 3), B(4, –2) and C(–1, –3). Graph △ABC and its image after a translation along〈–2, –1〉 and a
reflection in the x–axis.
27
Geometry
Section 9.5 Notes: Symmetry
Date:
Learning Targets:
1. I can identify line and rotational symmetries in two‐dimensional figures.
2. I can identify plane and axis symmetries in three‐dimensional figures.
If the images to the
right describe
symmetry, in your
own words, define
symmetry:
Symmetry
Line Symmetry
Line of Symmetry
State whether the object appears to have line symmetry. Write yes or no. If so, draw all lines of
symmetry, and state their number.
Example 1
a)
b)
c)
28
Rotational
Symmetry
Center of Symmetry
Order of Symmetry
Magnitude of
Symmetry
Example 2
State whether the figure has rotational symmetry. Write yes or no. If so, locate the center of symmetry,
and state the order and magnitude of symmetry.
a)
You Try!
b)
c)
State whether the figure has rotational symmetry. Write yes or no. If so, locate the center of symmetry,
and state the order and magnitude of symmetry.
29
Example 3
Determine whether the entire word has line symmetry and whether it has rotational symmetry.
Identify all lines of symmetry and angles of rotation that map the entire word onto itself.
Plane Symmetry
Axis Symmetry
Three Dimensional
Symmetries
30
Example 4
State whether the figure has plane symmetry, axis symmetry, both, or neither.
a)
You Try!
b)
State whether the figure has plane symmetry, axis symmetry, both, or neither.
1.
2.
3.
4.
31
5.
6.
32
33
9-5 Symmetry
State whether the figure appears to have line symmetry. Write yes or no. If so, draw all lines of symmetry and state their
number.
1.
2.
3.
State whether the figure has rotational symmetry. Write yes or no. If so, locate the center of symmetry, and state the order and
magnitude of symmetry.
4.
5.
6.
State whether the figure has plane symmetry, axis symmetry, both, or neither.
1.
2.
34
3.
4.
5.
6.
35
Geometry
Section 9.6 Notes: Dilations
Date:
Learning Targets:
1. I can draw dilations in the coordinate plane.
If the images to the
right describe a
translation, in your
own words, define
translation:
Dilations on a
Coordinate Plane
Scale Factor
Example 1
Trapezoid EFGH has vertices E(–8, 4), F(–4, 8), G(8, 4) and H(–4, –8). Graph the image of EFGH after
1
a dilation centered at the origin with a scale factor of .
4
36
Find the image of each polygon with the given vertices after a dilation centered at the origin with the
given scale factor.
Example 2
a. J(2, 4), K(4, 4), P(3, 2); r = 2
b. D(–2, 0), G(0, 2), F(2, –2); r = 1.5
Example 3
Leila drew a polygon with coordinates (–1, 2), (1, 2), (1, –2), and (–1, –2). She then dilated the image
and obtained another polygon with coordinates (–6, 12), (6, 12), (6, –12), and (–6, –12). What was the
scale factor and center of this dilation?
Example 4
Find the scale factor from the pre-image to the image for the following dilation. A(2,5), B(3,1), C(4,2) and A’(3, 7.5), B’(4.5, -1.5), C‘(6, 3).
37
Summary!
Nemo is located on the coordinate plane. Write down Nemo’s coordinate points here:
Marlin believes Nemo will be 3 times the size he is now. Dilate the Nemo using a scale factor of 3.
Write the coordinate points here:
Graph the dilated coordinate points and name them accordingly.
When you are finished, compare with your neighbor.
38
39
9-6 Dilations
Graph the image of each polygon with the given vertices after a dilation centered at the origin
with the given scale factor.
1. E(–2, –2), F(–2, 4), G(2, 4), H(2, –2);
2. A(0, 0), B(3, 3), C(6, 3), D(6, –3),
1
E(3, –3); r =
3
3. A(–2, –2), B(–1, 2), C(2, 1); r = 2
r = 0.5
40
4. A(2, 2), B(3, 4), C(5, 2); r = 2.5
5. A(–2, –2), B(1, –1), and C(2, 0). r = 2.
41