Created on: September 10, 2008

Website Address: https://library.curriki.org/oer/Lesson--Composition-of-Transformations

TABLE OF CONTENTS

- Curriki Project Based Geometry
- Curriki Calculus: Applications of Derivatives
- Curriki Calculus: Integrals

- Selling Geometry
- Designing a Winner
- What's Your Angle, Pythagoras?
- TED Talk: House of the Future
- The Art of Triangles
- How Random Is My Life?
- Introduction to Angles
- Lesson -- Drawing right triangles from word problems
- Accessing Curriki Geometry Projects
- Introduction to Curriki Geometry

- Selling Geometry Resources
- Curriki Geometry Tools and Resources
- Lesson -- Rotation
- The World Runs on Symmetry
- Lesson -- Dilations and Isometry
- Lesson -- Composition of Transformations
- Cool Math 4 Kids: Tessellations
- Tessellations.org
- Euclid
- About Cloze Notes
- What's the point of Geometry? - Euclid
- Selling Geometry Project Teacher Edition
- Selling Geometry Project Student Packet

- Applications of Derivatives Table of Contents by Standard
- AD.1: Find the slope of a curve at a point.
- AD.2: Find a tangent line to a curve at a point and a local linear approximation.
- AD.3: Decide where functions are decreasing and increasing.
- AD.4: Solve real-world and other mathematical problems involving extrema.
- AD.5: Analyze real-world problems modeled by curves.
- AD.6: Find points of inflection of functions.
- AD.7: Use first and second derivatives to help sketch graphs.
- AD.8: Compare the corresponding characteristics of the graphs of f, f', and f".
- AD.9: Solve optimization real-world problems with and without technology.
- AD.10: Find average and instantaneous rates of change.
- AD.11: Find the velocity and acceleration of a particle moving in a straight line.
- AD.12: Model rates of change, including related rates problems.
- AD.13: Interpret a derivative as a rate of change in applications.
- AD.14 Geometric interpretation of differential equations via slope fields

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?