Shape Transformation

Tim Brzezinski, Lee McCulloch-James, Apr 20, 2020

Transformational Geometry Applets, Discovery Learning Applets, etc...

Table of Contents

  1. Introduction
    1. Messing With the Mona Lisa
  2. Dilations
    1. Properties of Dilations
    2. Dilations of a star
    3. Exploring Dilations in the Coordinate Plane
    4. AA Similarity Theorem
  3. Translations
    1. Translations and Rotations
    2. Translations
    3. Examples of Translations on a coordinate plane
  4. Rotations
    1. Exploring Rotations
    2. Exploring Rotations on the Coordinate Plane
    3. Two rotations
    4. Rotational Symmetry of Quadrilaterals
    5. Order of rotational symmetry of regular polygons
  5. Reflection About a Line
    1. Daffy Reflection
    2. Image of Girl in the Mirror
    3. Exploring Reflections
    4. Reflections-Distances
  6. Reflection About a Point
    1. Reflection About a Point
    2. Transformations: Exercise 3
    3. Transformations: Exercise 1
  7. extended Vector-translations
    1. Translating Triangle by a Vector
    2. Vector Addition
  8. extended Matrix representation of Transformations
    1. Transformations
    2. Matrix Transformations
    3. Matrix Transformations
    4. Transformations: matrix
    5. Matrix Multiply transformation
  9. Function transformations
    1. Function Transformations
    2. Matrix Transformations

1.

Introduction

  • 1. Messing With the Mona Lisa

1.1.

Messing With the Mona Lisa

Note: LARGE POINTS are MOVEABLE.
– Lee McCulloch-James, Tim Brzezinski

2.

Dilations

  • 1. Properties of Dilations
  • 2. Dilations of a star
  • 3. Exploring Dilations in the Coordinate Plane
  • 4. AA Similarity Theorem

2.1.

Properties of Dilations

This applet accompanies the [b]Introduction to Dilations[/b] activity given to you in class.  [br]Have fun with this!  
– Tim Brzezinski

2.2.

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2.3.

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2.4.

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3.

Translations

  • 1. Translations and Rotations
  • 2. Translations
  • 3. Examples of Translations on a coordinate plane

3.1.

Translations and Rotations

Direct Isometries
Translations and rotations are [i]direct isometries[/i]. If you read the names of the vertices in cyclic order (A-B-C and A'-B'-C'), both would be read in the counterclockwise (or clockwise) direction.
Translation
Rotation
– Steve Phelps

3.2.

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3.3.

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4.

Rotations

  • 1. Exploring Rotations
  • 2. Exploring Rotations on the Coordinate Plane
  • 3. Two rotations
  • 4. Rotational Symmetry of Quadrilaterals
  • 5. Order of rotational symmetry of regular polygons

4.1.

Exploring Rotations

Exploring Rotations
– avery.js, leeb

4.2.

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4.3.

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4.4.

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4.5.

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5.

Reflection About a Line

  • 1. Daffy Reflection
  • 2. Image of Girl in the Mirror
  • 3. Exploring Reflections
  • 4. Reflections-Distances

5.1.

Daffy Reflection

[size=150][b][color=#1e84cc]Is the preimage (AB) Daffy congruent with the image (A[/color][/b][math]'[/math][b][color=#1e84cc]B[/color][/b][math]'[/math][b][color=#1e84cc])Daffy?[/color][/b] [/size]
[color=#b45f06][size=200][size=150][b]Move point C on line CD to the left and right. What happens to the image?[/b][/size][/size] [/color]
[b][color=#9900ff][size=150]Move point C on line CD to the left and right. What happens to the image? [/size][/color][/b]
[b][size=150][color=#38761d]Click and hold on preimage Daffy. Move the preimage toward the reflection line. What happens to image Daffy?[/color][/size][/b]
[b][size=150][color=#85200c]Click and hold on preimage Daffy. Move the preimage away from the reflection line. What happens to image Daffy? [/color][/size][/b]
– Lee McCulloch-James, Judith Hilinski

5.2.

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5.3.

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5.4.

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6.

Reflection About a Point

  • 1. Reflection About a Point
  • 2. Transformations: Exercise 3
  • 3. Transformations: Exercise 1

6.1.

Reflection About a Point

Reflection About a Point:
– Gregory Kusmitch

6.2.

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6.3.

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7.

extended Vector-translations

  • 1. Translating Triangle by a Vector
  • 2. Vector Addition

7.1.

Translating Triangle by a Vector

Play through the construction of the translation by a vector.[br]Which points can you move? Which points can't be moved? Why?
– Lee McCulloch-James, Steve Phelps

7.2.

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8.

extended Matrix representation of Transformations

  • 1. Transformations
  • 2. Matrix Transformations
  • 3. Matrix Transformations
  • 4. Transformations: matrix
  • 5. Matrix Multiply transformation

8.1.

Transformations

Describing Transformations[br][br]Rotation - centre, angle & direction (clockwise or anti-clockwise)[br]Reflection - the line of reflection[br]Enlargement - centre & scale factor[br]Translation - vector
– DavidA

8.2.

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8.3.

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8.4.

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8.5.

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9.

Function transformations

  • 1. Function Transformations
  • 2. Matrix Transformations

9.1.

Function Transformations

[b]We often explore four types of function translations: reflections across the x-axis, vertical stretches, horizontal shifts, and vertical shifts. For a function f(x), a translated function g(x) often takes the form g(x)=a f(x+b)+c. Explore the following functions, using the appropriate sliders, to determine how the values of a, b, and c define function translations for many functions.[/b]
[b]1) Define a in terms of the four function translations mentioned above.[/b]
[b]2) Define b in terms of the four function translations mentioned above.[/b]
[b]3) Define c in terms of the four function translations mentioned above.[/b]
– Mark Beckwith

9.2.

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