Lesson -- Composition of Transformations

Lesson: Composition of Transformations

Prerequisite Knowledge: Students should be familiar with reflections, dilations, rotations and translations. They should also be familiar with isometry.

Learning Objectives: Students will be able to perform more than one transformation with regular polygons on a coordinate plane. Students will understand the concept of a glide reflection.

Key Ideas: A special two step transformation called a glide transformation consists of a translation and then a reflection. The line of reflection must be parallel to the direction of the translation.

Motivational Problem: Have students plot the points A(-1,0) B(4,0) and C(2,6). First have them perform the transformation T(4, -3). Tell the students to label the new points A’B’C’. They should also record the new coordinates. Next have the students transform triangle A’B’C’ under T(3, 2). Tell the students to record the new coordinates and label the new figure A’’B’’C’’. Then have them answer these questions.

1. How would I transform A’’B’’C’’ back to the original figure?

2. If I wanted to give directions to combine both translations into one transformation, what would the directions be? Show your calculations or write down an explanation.

Important Questions: What can you say about the congruence of the preimage (original figure) and the image after multiple transformations?