Transformations

Ben Dougherty, Jun 26, 2014

Table of Contents

  1. Translations
    1. Raytown Translation - 2
    2. Translation of a figure
  2. Reflections
    1. Triangle Reflection Exploration
    2. What's My Rule #3?
    3. What's My Rule #4?
    4. What's My Number Line Rule #7?
    5. Reflecting Polygons Over the Axes
  3. Rotations
    1. Triangle Rotation Example
    2. What's My Rule #5?
  4. Dilations
    1. Triangle Dilation
    2. What's My Rule #7?
    3. What's My Number Line Rule #4?
  5. Tessellations
    1. Tessellation by Translation
    2. Tessellation by Translation Demonstration

1.

Translations

  • 1. Raytown Translation - 2
  • 2. Translation of a figure

1.1.

Raytown Translation - 2

Students explore and discover what happens to a new shape under a translation.
Today our goal is to determine what happens to a shapes pre-image (red) to an image (blue) under a specific translation.[br][br]As you move the slider around....[br][br]1. Does the image change size? Explain[br][br]2. Does the image change shape? Explain[br][br]3. Do the points change? Explain[br][br]4. Describe the change in the coordinates from the pre-image to the image.[br][br]5. Create a rule from your statement above?[br][br]6. What would you call this translation?
– zeyk

1.2.

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2.

Reflections

  • 1. Triangle Reflection Exploration
  • 2. What's My Rule #3?
  • 3. What's My Rule #4?
  • 4. What's My Number Line Rule #7?
  • 5. Reflecting Polygons Over the Axes

2.1.

Triangle Reflection Exploration

Use the slider to explore how changing triangle ABA' impacts its reflection (triangle A'B'A''). Are the two triangles congruent? If you connect B to B' with a segment, how would segment BB' be related to line GH?
– Ben Dougherty

2.2.

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2.3.

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2.4.

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2.5.

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3.

Rotations

  • 1. Triangle Rotation Example
  • 2. What's My Rule #5?

3.1.

Triangle Rotation Example

The slider controls of the angle of rotation of triangle ABC around the origin, which is A'B'C'. Move the slider to see how the triangle rotates.

1) What are the coordinates of A', B', and C' when r = 90º? 2) What are the coordinates of A',B', and C' when r = 180º? 3) What are the coordinates of A',B', and C' when r = 270º? 4) What are the coordinates of A',B', and C' when r = 360º? 5) What patterns do you recognize to transform A to A' for each of these transformations?
– Ben Dougherty

3.2.

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4.

Dilations

  • 1. Triangle Dilation
  • 2. What's My Rule #7?
  • 3. What's My Number Line Rule #4?

4.1.

Triangle Dilation

Use the slider to control "k" which is the scale factor of the dilation of triangle ABC to triangle A'B'C'.

1) If k = 1, how does triangle ABC compare to triangle A'B'C'? 2) If k = 2, how does triangle ABC compare to triangle A'B'C'? 3) If k = .5, how does triangle ABC compare to triangle A'B'C'? 4) What is the difference between dilating the triangle k = 2 and k = -2?
– Ben Dougherty

4.2.

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4.3.

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5.

Tessellations

  • 1. Tessellation by Translation
  • 2. Tessellation by Translation Demonstration

5.1.

Tessellation by Translation

Play through construction of the translations.
Tessellation by Translation
– Steve Phelps

5.2.

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