Created on: September 10, 2008

Website Address: https://library.curriki.org/oer/Lesson--Dilations-and-Isometry

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

- Maximum and Minimum Values of Curves and optimization
- Optimization
- Maximum-Minimum Problems: Business and Economics Applications, Part 1
- Maximum-Minimum Problems: Business and Economics Applications, Part 2
- Optimization Problems
- Extreme Values on Intervals
- Maximum & Minimum Vales and Optimization Exercises
- Relative Minima and Maxima Exercises
- Absolute Extrema Exercises
- Optimization Exercises
- Local Extreme Values Exercises
- Endpoint and Absolute Extreme Values Exercises

Lesson: Dilation and Isometries

Prerequisite Knowledge: Students should be familiar with reflections, rotations and translations. Students should be familiar with graphing on the coordinate plane.

Learning Objectives: Students will be able to identify and perform a dilation on the coordinate plane. Students will be able to understand the scale factor of dilation. Students will understand the concept of isometry and apply it to reflection, rotation and translation.

Key Ideas: Dilation (x,y) D scale of 4 (4x,4y)

The scale factor can refer to an enlargement or a reduction of a figure

Motivational
Problem: On a coordinate plane plot the points A(-2,0) B(-2,2) C(-1,2) and
D(0,-1). Perform the translation T(4,
-2). Plot the new points and record the
new coordinates labeling them A’B’C’. With the **original figure**
multiple each x,y coordinate by 3. Plot and record the new coordinates labeling
them A’’B’’C’’. Answer the following
questions about the new figures:

Important Questions: What is a scalar?