Concept explainers
To find: Whether any points are invariant under the glide reflections and under the composition of transformations.
Answer to Problem 39HP
The invariant points in the graph and the points may remain invariant under the composition of the transformation. There may be an invariant point in the figure as it is rotated or reflected, rotated twice and reflected twice.
Explanation of Solution
Consider the glide reflection shown below in Figure 1
Figure 1
There are no invariant points in the graph and the points may remain invariant under the composition of the transformation. There may be an invariant point in the figure as it is rotated or reflected, rotated twice and reflected twice.
Consider the diagram for the two 180 degree rotation as shown in Figure 2
Figure 2
Consider the figure for two reflection about the same line as shown in Figure 3
Figure 3
The image can be obtained back to the original image by rotation and reflection. Thus, the
Figure 4
Chapter 9 Solutions
Geometry, Student Edition
Additional Math Textbook Solutions
Elementary Statistics: Picturing the World (7th Edition)
Calculus and Its Applications (11th Edition)
University Calculus: Early Transcendentals (3rd Edition)
Fundamentals of Statistics (5th Edition)
Elementary Algebra
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning