Name
Date
Puzzle Time What Can Go Up The Chimney Down, But Not Down The Ghimney Up? Write the letter of each answer in the box containing the exercise number.
Answers
Complete the following questions.
1. What 2.
A.4 '2
is another name for the original figure?
A translation is a
3.A
?
is a quantity that has both direction and
magnitude, or size.
Find the coordinates of the preimage.
4. (*, y)
-.
A'(3,3)
(x + 3, y
-
B'(-2,
4)
and
S)
with endpoints
5. (t, y) - (r - l, y + 3)with endpoints A'(-2,0)
and
B'(5, -4)
Find the rule for the translation of the coordinates.
6. 7.
f. (",y) -+ (x + 2,y Y. A(-3, -6), B(4, -t) U.
vector
L.
A(6, -2), B(-1, -1)
N. (r,l) -(r+4,y+2)
v.
1
E. A(-t,
-3), 8(6, -7)
F.0
-4) -+ A'(1, -8) B(4,6) -+ n'(2, z)
B. l(0, 8), B(-5, 9)
A\-6. -4) --> ,t'(-2. -Z) B(2, 5) -+ a'(6,7)
M. (*,y) - (, - 2,y -
A(3,
(-a, Z)describes the translations A(-1,x) -+ A'(-4y,1) and B(22 - 1, 1) + B'(3,3).
The vector
T.
image
L. -l K.
flexible motion preimage
Find the value of-r.
R.
9.
Find the value ofy.
L.
10. Find the value of z.
O.
line
A.
rigid motion
1
P. (r,y) - (* - 4,y Geometry Resources by Chapter
4)
G.2
8.
114
a)
2)
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Name
Date
Practice A 1.
Name the vector and write its component form.
The vertices
of LABC
the vector (t,
3.
4.
are
A(2,3), B(-1, 2), andC(0, 1). Translate A,4BC using
-+). Graph LABC
and its image.
Find the component form of the vector that translates
-2)
to
A'(-1. a).
Write a rule for the translation
of ARSI to AR'S?'.
f
n Exercises 5 and 6, use the translation
(r, y)
-
(x +
1,
V
-
3) to find the image
of the given point.
5.
6. M(-3, -8)
Q(s,9)
ln Exercises 7 and 8, graph ACDE with vertices C(-1, 3), D(0, -2), and E(1, 1) and its image after the given translation or composition.
7. Translation:
9.
(x.
y)
+ (r -
3.
y+
l)
y) -+ Translation: (*, y) -
8. Translation:
You want to plot the collinear points A(-2, 3), A'(x,
y),
and
(x,
(i* (x-
A"(3, 7) on the
10,y
-
7,y +
8)
15)
same
coordinate plane. Do you have enough information to find the values of x and y? Explain your reasoning.
10. You are using the map
shown to navigate through the city. You decide to walk to the Post Office from your current location at the Community Center. Describe the translation that you will follow. If each grid on the map is 0.05 mile, how far will you travel?
{omrnunity aenter
3
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Geometry 111 Resources by Chapter
Name
Date
&Puzzterime What Type Of Dance Does A Geometry Teacher Like? Circle the letter of each correct answer in the boxes below. The circled letters out the answer to the riddle.
will spell
Complete the sentence.
1.A
is a transformation that uses a line like a mirror to reflect the figure.
2. If
(a, b) is reflected in the x-axis, then its image is the point
3. If
(a, 6) is reflected in the line y
4.4
reflection is
a
= x, then its image is the point
transformation involving a translation followed by a reflection.
5. A figure in the plane has line
when the figure can be mapped onto itself by
a reflection in a hne.
How many lines of symmetry does the figure have?
ldentify the vertices of the image created after the reflection in the given line.
s. A(3,4),8(s,2),!=x 10. A(6, -3), B(-2, 4);
.x-axis
11. A(-2, -t), B(3,9),
!
= -x
H
S
K
L
o
U
W
9
(b, o)
l6
7
0
symmetry
slider
G
I
D
F
o
A
D
N
6
4.5
reflection
rotation
A'(r,2), B'(-9, -3)
A'(3,-4), B'(5,
-2)
(-b'-o) (",-b)
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I
A'(1,
-2),
B'(3,
-e)
A
R
2
5
B'(-2, -4)
E
c
E
A'(4,3), B'(2, s)
glide
E
A'(6, 3),
1
t
Geometry { 19 Resources by Chapter
Name
Date
@PracticeA ln Exercises 1-3, graph LABC and its image after a reflection in the given line.
1. A(0,2), B(1, -3), C(2, 4); r-aris 2. A(-2, 3.
-4), 8(6,2), C(3, -5); y-axis
A(4, -t), B(3, 8), C(-1,
1);
!
= -2
ln Exercises 4 and 5, graph the polygon and its image after a reflection in the given line.
4' !=-s
ln Exercises 6 and 7, graph AJKL with vertices J(2, 3), K(-2,1), and L(-1, 5) and its image after the glide reflection.
6. Translation:
(x,
y) -+ (, -
l,,y)
Reflection: in the x-axis
7. Translation:
(x,
y)
-->
Reflection: in the line
(t + 2, y -
3)
x = -2
ln Exercises 8 and 9, determine the number of lines of symmetry for the figure.
8A \/
AA V
10.
Find point W on lhe y-axis so that VW + XW is a minimum given Z(2, 3) and
11.
x(-2, -t). A line y = 3x -
5 is reflected in x = a
so that the image is given
by
y=I-
3x.
What is the value of a?
12. Your friend claims
that it is not possible to have a glide reflection if you have two translations followed by one reflection. Is your friend correct? Explain your reasoning.
115
Geometry Resources by Chapter
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Date
Name
Puzzle Time What Did One Parallel Line Say To The Other Parallel Line? c
B
A
E
D
F
tt
Gomplete each exercise. Find the answer in the answer column. Write the word under the answer in the box containing the exercise letter. (1,1) MEET
A.A
is a transformation in which a figure is turned about a fixed point.
symmetric AND
(-a' -b) SHAME
C.
When a point (a, b) is rotated counterclockwise about the origin for a rotation of 180o, (a, b) --> (_ )
WILL
D.
When a point (a, b) is rotated counterclockwise about the
NAMED
(a, bl DOWN
STRAIGHT
When a point (a, b) is rotated counterclockwise about the origin for a rotation of 90o, (a, b) --> ()
B.
rotation WHAT
(-a, -a)
Complete the sentence.
(5, 3)
(-1 , -1)
originforarotation of 270o,(a,b) -+
(-)
-5)
(-b,
SKINNY
A
(3,
Triangle ABC has vertices A(-3, 5), B(4, 3), and C(-1, 1)' Find the vertex of the image after a 270o rotation about the
(3,
-4)
NEVER
origin.
a)
(0,0) DEEP
E. A, (b,
-a)
(3, 4)
F.
B,
G.
C'
WE
124
Geometry Resources by Chapter
LONG
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Date
Name
Practice A 1. Trace point
the polygon and point P. Then draw a 60" rotation ofthe polygon about
P.
A
.P
2.
Graph the polygon and its image after a 270o rotation about the origin.
i:: |
.M,
ln Exercises 3 and 4, graph ARSI with vertices R(2, 3), S(-2,
1),
and
f(-1,
5)
and its image after the composition.
3. Translation:
(x,
y) -+ (t
-
2,
Rotation: 90o about the origin
y
-
l)
4.
Reflection: in the line
x=
-],
Rotation: 180" about the origin
ln Exercises 5 and 6, determine whether the figure has rotational symmetry. lf so, describe any rotations that map the figure onto itself.
7.
Draw AB with points A(2,0) and B(0, 2). Rotate the segment 90o counterclockwise about point l. Then rotate the two segments 180o about the origin. What geometric figure did you create using the original segment and its images?
8. List the uppercase letters of the alphabet that have rotational symmetry, and state the
angle of the symmetry.
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Geometry 121 Resources by Chapter
Date
Name
Puzzle Time What Geometric Figure ls Like A Lost Parrot? Write the letter of each answer in the box containing the exercise number.
1. Complete the sentence. Two geometric
figures are
_
figures
if and only if there is a rigid motion or a composition of rigid
Answers
motions that maps one of the figures onto the other.
R.
2.
Congruent figures have the same size and shape. True or false?
3.
Are three equilateral triangles with respective sides
of
L
are not
constructed
N. (6,-6)
3 centimeters, 4 centimeters, and 4 inches congruent? Yes or no?
M.
yes
in line ft, and the image is then reflected in line m. The measure of the acute angle formed between lines k and m is 42". What is the angle of rotation?
A.
are
B.
(2,6)
Given AABC with vertices A(2,3), B(4, 3), and C(4, -5), and the translation (t, y) - (x + 2, y - 1), find the vertex of the image.
c.
(4,2)
L.
84
P.
no
E.
48
O.
true
x.
(2,4)
Y.
congruent
o.
(6,2)
u.
(-6,
4. A figure is reflected
5.
A'
6.
B'
7.
C'
8.
Complete the sentence. The polygons with verlices A(0,7),
B(0, 4), C(5, 4), D(5,7) and E(7,3), F(7,0), G(i2, 0),
H(12,3)
congruent.
8
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3
6
4
1
5
2
6)
7
Geometry 129 Resources by Chapter
Date
Name
@PracticeA f
n Exercises 1 and 2, identify any congruent figures in the coordinate plane. Explain.
#E -6
-4
ln Exercises 3 and 4, describe a congruence transformation that maps AABC AA'B'C'.
to
3.
ln Exercises 5 and 6, determine whether the polygons with the given vertices are congruent. Use transformations to explain your reasoning.
5.
A(5, 2), B(2, 2), c(2, 7) and
6.
E(6, -2), F(10, -2), c(l0, -8),11(6, -8) andw(4,8), x(4, 10), r(8, 10), z(s,
7.
In the figure,
s(-4, -5), r(-1, -5), u(-1,
0)
a ll
b, LCDE is reflected in line a, and LC'D'E'is reflected in line D. List three pairs of segments that are parallel to each other. Then determine whether any segments are congruentto EE".
ln Exercises 8 and 9, find the measure of the acute or right angle formed by intersecting lines so that P can be mapped to P" using two reflections.
8. A rotation of 28" maps P to P". 9.
{26
The rotation (r,
y) - (-y, ")
Geometry Resources by Chapter
8)
,4, C
unE
C'U
maps P to P".
a
\/ \/ A
./\
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Name
Date
&
Puzzterime
What Side Of A House Gets The Most Rain? Circle the letter of each correct answer in the boxes below. The circled letters out the answet to the riddle.
will
spell
Complete the sentence or solve the problem.
1.A
is a transformation in which a figure is enlarged or reduced with respect to a fixed point C, called the center, and a scale factor k, which is the
ratio of the lengths of the corresponding sides of the image and the preimage. 2.
When the scale factor
3.
When
0
1,
k > 1, a dilation
is a(n)
adilationisa(n)
4. When a transformation changes the shape or size of a figure, the transformation is
5.
You want to reduce a picture that is l0 inches by 12 inches to a picture that is 2.5 inches by 3 inches. What is the scale factor k?
6. A magnifzing glass shows
the image of an object that is 10 times the object's actual size. Determine the length of the image of the object if the actual length of the object is 8 millimeters.
7.
A magnif,ing glass shows the image of an object that is 6 times the object's actual size. Determine the actual length of the object if the image is 120 millimeters.
Find the coordinates of the vertices after a dilation centered at the origin with
scalefactor
8.
k=-+. e.
A(3,6)
R
T
(-3, -6)
80 mm
G
I
8
4
134
10. c(e. 0)
B(3,3)
L
a
H
E
M
A
o
40
:xpansion
dilation
(-1,-1)
alteration
shrink
reduction
U
T
P
s
I
N
D
E
(-3,0)
20 mm
(l,r)
enlargement
rigid
(-r,-2)
nonrigid
K
(-e,
0)
Geometry Resources by Chapter
I
1
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Date
Name
Practice A ln Exercises 1 and 2, find the scale factor of the dilation. Then tell whether the difation is a reduction or an enlargement. 1.
P'
ln Exercises 3-5, copy the diagram. Then use a compass and straightedge to construct a dilation of quadrilateral ABCD with the given center and scale factor k.
3.
Center B,
4.
Center
5.
Center C,
k=
3
p. k = +
k=
75oA
ln Exercises 6 and 7, graph the polygon and its image after a dilation with a scale factor k.
k=2
6.
P(r,2), Q(2,2), R(4, -2), S(-1, -3);
7.
A(-4,4), B(-2,6), C(1, -1), D(-2, -4); k = -t5oh
8. A stardard
piece of paper is 8.5 inches by 11 inches. A piece of legal-size paper is 8.5 inches by 14 inches. By what scale factor k would you need to dilate the standard paper so that you could fit two pages on a single piece oflegal paper?
9.
The old film-style cameras created photos that were best printed at 3.5 inches by 5 inches. Today's new digital cameras create photos that are best printed at 4 inches by 6 inches. Neither size picture will scale perfectly to fit in an 1l-inch by l4-inch frame. Which type of camera will you minimize the loss ofthe edges ofyour picture?
l-=
B.s
in.---l
lillrtiL rt lr,r::rri.r\\#iift
I =P; i'il lft
= r:=
14 in. : i:i:iiiJ:ffilttSllltlV:r:::::#i
i fiil '*
ll::,o.=.:w"rrl
tii 1=:
rLi
iiriii:i:::::::::l.,Znililil,.....u:::ir:i
10. Your friend claims
that if you dilate a rectangle by a certain scale factor, then the area of the ob.ject also increases or decreases by the same amount. ls your friend correct? Explain your reasoning.
11
.
Would it make sense to state "A dilation has a scale factor of 1?" Explain your reasoning.
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Geometry 131 Resources by Chapter
Date
Name
Puzzle Time Why Did The Students Do Multiplication Problems On The Floor? A
B
G
H
c
D
F
E
Complete each exercise. Find the answer in the answer column. Write the word under the answer in the box containing the exercise letter. false
Gomplete the sentence.
dilation
NOT
A.
not similar AND
B.
transformations preserve length and angle measure.
c.
transformations preserve angle measure only.
not maintain BECAUSE
3), C(7,
TO
TEACHER
o),4(9, 3) and yes THEM
Yes or no?
E. A(4,4), B(7,2),
congruence
CLASS
R(0, 3), S(-2, o), T(2, -3), U(4, o)
nay
STAY
not always
Determine whether the following are congruent.
D. A(s, 6),8(3,
always TABLES
_
figures when they have the same shape but not necessarily the same size.
Two figures are
C(s, -2), n(t,2) and
yea
R(-8, -8), ,s(r4, -4), z(-10, 4), u(2, -4)
GOT
True or false? transitional FLOOR
F.
maintain
A(3,6), 8(6,3), C(-3, 3)
and
R(-1, -2), s(-2, -1), z(r, true
USE
-t) no BAD
Yea or nay?
CUSTODIAN
Answer the question. similarity
G. If a triangle is transformed factor
TOLD
by a dilation with a scale
of -1, will it maintain congruency or not maintain
similar THE
congruency?
H.
Do similarity transformations preserve angle measure always or not always?
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Geometry {39 Resources by Chapter
Name
Date
!!|PracticeA fn Exercises 1and2, graph APQRwith verticesP(-1, 5), Q(-4, 3), and R(-2,
I
and its image after the similarity transformation.
1. Rotation: 180o abouttheorigin Dilation:
3.
(",y) -
(Zx,
Zy)
2. Dilation: (r,:') -+ (!*,
+t
Reflection: inthex-axis
Describe a similarity transformation that maps the black preimage onto the dashed image.
ln Exercises 4 and 5, determine whether the polygons with the given vertices are similar. Use transformations to explain your reasoning.
4.
A(-2, 5), B(-2,2), c(-1,2) and D(3, 3), E(3, t), F(2,1)
6.
s. J(-s, -3), K(-3, -1), L(-3, -5), M(-5,
-5)
and
T(3,3), u(4,3), v(4,2), w(3, t)
Prove that the figures are similar.
Given
Equilateral LGHI with side length a, equilateral LPQR with side length 6
Prove LGHI is similar to LPQR.
0
a",< R
7. Your friend claims you can use a similarity transformation to tum a square into a rectangle. [s your friend correct? Explain your answer. 8. Is the composition of a dilation and a translation commutative? In other words, do you obtain the same image regardless of the order in which the transformations are performed? Justify your answer.
9.
135
The image shown is known as a Sierpinski triangle. It is a common mathematical construct in the area of fractals. What can you say about the similarity transformations used to create the white triangles in this image?
Geometry Resources by Chapter
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