Transformations
and Symmetry
Essential Question: How can you use
transformations to solve real-world problems?
17
MODULE
LESSON 17.1
Translations
LESSON 17.2
Reflections
LESSON 17.3
Rotations
LESSON 17.4
© Houghton Mifflin Harcourt Publishing Company • Image Credits: ©Helen
King/Corbis
Investigating
Symmetry
REAL WORLD VIDEO
Check out how transformations
can be used to cut patterns out of
fabric as efficiently as possible.
MODULE PERFORMANCE TASK PREVIEW
Animating Digital Images
In this module, you will use transformations to create a simple
animation of a bird in flight. How do computer animators use
translations, rotations, and reflections? Let’s find out.
Module 17
831
Are YOU Ready?
Complete these exercises to review the skills you will need
for this module.
Properties of Reflections
Example 1
A figure in the first quadrant is reflected over the x-axis.
What quadrant is the image in?
• Online Homework
• Hints and Help
• Extra Practice
The image is in the fourth quadrant. A figure drawn on tracing
paper can be reflected across the x-axis by folding the paper
along the axis.
Find the quadrant of each image.
1.
The image from reflecting a figure in the first quadrant over the y-axis
2.
The image from reflecting a figure in the second quadrant over the x-axis
Properties of Rotations
Example 2
A figure in the first quadrant is rotated 90° counterclockwise
around the origin. What quadrant is the image in?
The image is in the second quadrant. In the second quadrant, each point of the figure
forms a clockwise 90° angle around the origin with its corresponding point in the
original figure.
Find the quadrant of each image.
3.
The image from rotating a figure in the third quadrant 180° clockwise
4.
The image from rotating a figure in the first quadrant 360° clockwise
Properties of Translations
A figure in the first quadrant is translated up 3 units and to
the right 1 unit. What quadrant is the image in?
The image is in the first quadrant. A translation only moves
the image in a direction; the image is not reflected or rotated.
Answer each question.
5.
A figure in the first quadrant is translated down and to the right. Is it known what quadrant the
image is in?
6.
A figure is translated 3 units up and 2 units left. How large is the image in comparison to
the figure?
Module 17
832
© Houghton Mifflin Harcourt Publishing Company
Example 3