Name
Date
Class
Practice B
LESSON
1-7
Transformations in the Coordinate Plane
Use the figure for Exercises 1–3.
The figure in the plane at right shows the preimage in the transformation
ABCD → ABCD. Match the number of the image (below) with the
name of the correct transformation.
Y
Y
X
Y
Y
!
"
$
#
"g
$g
#g
!g
"g
1. rotation
#g
X
2
$g X
"g
!g
!g
#g
$g X
2. translation
1
4. A figure has vertices at D(2, 1), E(3, 3), and F(0, 3).
After a transformation, the image of the figure has
vertices at D (1, 2), E(3, 3), and F(3, 0).
Draw the preimage and the image. Then identify
the transformation.
3
3. reflection
Y
X
rotation
5. A figure has vertices at G(0, 0), H(1, 2), I(1.5, 0),
and J(2.5, 2). Find the coordinates for the image of
GHIJ after the translation (x, y) → (x 2.5, y 4).
G(2.5, 4), H (3.5, 2), I(4, 4), J(5, 6)
Use the figure for Exercise 6.
Y
6. A parking garage attendant will make the most money when
the maximum number of cars fits in the parking garage. To fit
one more car in, the attendant moves a car from position 1 to
position 2. Write a rule for this translation.
X
(x, y) → (x 7, y 5)
7. A figure has vertices at X (1, 1), Y(2, 3), and Z(0, 4).
Draw the image of XYZ after the translation (x, y) → (x 2, y)
and a 180° rotation around X.
Y
X
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52
Holt Geometry
Name
Date
Class
Name
Practice A
LESSON
1-7
1-7
Complete the statements.
The figure in the plane at right shows the preimage in the transformation
ABCD � A�B�C�D�. Match the number of the image (below) with the
name of the correct transformation.
is the movement of a figure from its original position
original
position is called the preimage. The new position
image
is called the
�
slide
) is a transformation in which all the
4. A translation (or
points of a figure move the same distance in the same direction.
(or turn) is a transformation about a point.
�
�
�
��
�
�
�
�
�� ��
��
�
�
��
�
�
�
��
��
�
6. rotation
�
��
�
�
�
�
��
��
�
� ��
�
�� ��
��
��
�
�
��
�� �
��
��
��
��
�� ��
�
�
�
2
1
2. translation
3
9. A figure has vertices at X(3, �3), Y(1, �2),
and Z(3, 0). After a transformation, the
image of the figure has vertices at
X �(�3, �3), Y �(�1, �2), and Z �(�3, 0).
Draw the preimage and the image.
Then identify the transformation.
�
�
�� �
�
��
� � ��
��
��
��
�
�
�
�
��
�
reflection
��
��
�
�
�
��
(x, y) � (x � 7, y � 5)
�
�
��
�
�
51
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LESSON
1-7
Date
Holt Geometry
Class
Name
Practice C
�
1-7
�
��
�PQR
�
2. Tell how the image and preimage of the triangle do not match
up after the rotation mentioned in Exercise 1.
Reflection
Rotation
�
�
��
�
��
��
��
��
��
�JKL � �J�K �L�
�RST � �R �S �T �
A figure is flipped over
a line.
A figure is turned around
a fixed point.
A figure is slid to a new
position without turning.
1.
(�x, �y )
5. Determine the coordinates of any point A(x, y) rotated
90� clockwise around the origin.
(y, �x)
6. Determine the coordinates of any point A(x, y) rotated
180� clockwise around the origin.
(�x, �y)
2.
��
��
�
�
��
��
��
�
��
�
(x, y)
3.
�
�
translation; possible answer:
�FGH � �F �G �H�
reflection; possible answer:
�MNP � �M�N�P�
�
4. �
�
�
�
�
��
The Gulf Stream is a current in the Atlantic Ocean that flows up the eastern shore of
North America. The current mixes warm water from the Caribbean Sea with cooler
water in the North Sea. In doing so, the Gulf Stream helps warm Europe. The Gulf
Stream flows up to 2 meters per second in a northeasterly direction. Assume the
�
current flows �3 meters per second east (in the x direction) and 1 meter per second
north (in the y direction). Note that the Pythagorean Theorem shows that these result in
a movement 2 meters per second northeast. A jellyfish bobs along moved only by the current.
�
��
�
(x, y) � (x � �3, y � 1)
��
��
��
��
��
reflection; possible answer:
�WXY � �W�X �Y�
8. Write a rule for the translation the jellyfish goes through every second.
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�
�ABC � �A�B �C�
Find the coordinates.
53
�
�
Identify each transformation. Then use arrow notation to describe the
transformation.
�ABC and �PQR
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All rights reserved.
��
��
and Q moves to P�.
9. Find how many meters the jellyfish will travel in 1 minute.
�
��
3. Imagine �ABC and �PQR reflected across the y-axis and then the
x-axis. Name which triangle(s) can be rotated so that the image
exactly covers the preimage.
7. Determine the coordinates of any point A(x, y) reflected
across the x-axis and then across the y-axis and then
rotated 180� around the origin. (Hint: Use your answers
to Exercises 4 and 6.)
�
��
�
��
The vertex labels do not match. For the rotation, P moves to Q�
4. Determine the coordinates of any point A(x, y) reflected
across the x-axis and then across the y-axis.
Translation
��
�
�
�
Holt Geometry
Transformations in the Coordinate Plane
�� ��
�� �� �
�
�
Class
�
��
In a transformation, each point of a figure is moved to a new position.
�
1. Draw the images of �ABC and �PQR reflected across the
y-axis. Tell which triangle(s) can be rotated so that the rotation
image exactly covers the reflection image.
Date
�
Reteach
LESSON
Transformations in the Coordinate Plane
Use the figure for Exercises 1–3.
52
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All rights reserved.
�
�
�
��
Name
�
��
7. A figure has vertices at X (�1, 1), Y(�2, 3), and Z(0, 4).
Draw the image of XYZ after the translation (x, y) � (x � 2, y)
and a 180° rotation around X.
�
�
�
�
�
6. A parking garage attendant will make the most money when
the maximum number of cars fits in the parking garage. To fit
one more car in, the attendant moves a car from position 1 to
position 2. Write a rule for this translation.
�
�
�
��
�
�
Use the figure for Exercise 6.
��� �
��
�
�
G�(�2.5, 4), H�(�3.5, 2), I�(�4, 4), J�(�5, 6)
�HIJ � �H �I�J �
�
��
��
10. Draw and label the image of STUV
after the translation (x, y) � (x, y � 5).
1
8. reflection
�
5. A figure has vertices at G(0, 0), H(�1, �2), I(�1.5, 0),
and J(�2.5, 2). Find the coordinates for the image of
GHIJ after the translation (x, y) � (x � 2.5, y � 4).
�
�PQR � �P�Q�R�
3
3. reflection
rotation
�
7. translation
ABCD � A�B �C�D�
�
�
�
��
�
2
�
�
��
�
4. A figure has vertices at D(�2, 1), E(�3, 3), and F(0, 3).
After a transformation, the image of the figure has
vertices at D �(�1, �2), E�(�3, �3), and F �(�3, 0).
Draw the preimage and the image. Then identify
the transformation.
��
��
�
��
��
1. rotation
�
�
��
�� �
��
�
��
�
��
�
�
��
�
Match the number below each diagram with the name of the transformation
pictured. Then use arrow notation to describe each transformation.
�
�
��
(or flip) is a transformation across a line.
rotation
�
�
�
.
��
reflection
5. A
Transformations in the Coordinate Plane
Use the figure for Exercises 1–3.
transformation
1. A
to a new position.
3. A
Class
Practice B
LESSON
Transformations in the Coordinate Plane
2. The
Date
rotation; possible answer:
�ABCD � �A�B�C�D �
120 meters
Holt Geometry
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54
Holt Geometry
Holt Geometry