Lesson: Composition of Transformations
Students should be familiar with reflections, dilations, rotations and
translations. They should also be
familiar with isometry.
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.
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
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.
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
Questions: What can you say about the congruence of the preimage (original
figure) and the image after multiple transformations?