Lesson 4: 3-4: Compositions of Transformations

1. When analyzing an image and preimage, what can you look for to determine which transformation had been applied?
2. When performing a composition of transformations, does the order the transformations are performed affect the final image?
3. Describe a composition of transformations that could be performed in a single transformation.

Composition of Transformations
Glide Reflection

G.CO.2
Represent transformations in the plane using e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
G.CO.5
Given a geometric figure and a rotation, reflections, or translation, draw the transformed figure. Specify a sequence of transformations that will carry a given figure onto another.

When a transformation is applied to a figure, and then another transformation is applied to its image, the resulting transformation is called a composition of transformations. A glide reflection is a translation followed by a reflection in a line parallel to the translation vector.

The pattern of footprints left in the sand after a person walks along the edge of a beach illustrates the composition of two different transformations - translations and reflections.

Students approaching grade level can be given practice problems in small groups to work with other students or directly with the teacher.
Students beyond grade level can make deeper connections in the following way: working together to connect art and geometry. Give students a preimage and have them create an artistic picture using multiple transformations, while keeping track of the transformations they are performing.

Formative Assessment

Textbook in class

Access online textbook and resources through class link.