Geometric Transformations

akruizenga, Mar 18, 2016

Explore coordinate rules for reflections (across the axes and lines y=x and y=-x), translations, and rotations about the origin (90, 180, and 270 degrees)

Table of Contents

  1. Reflections
    1. Reflecting across the x-axis
    2. Reflecting across the y-axis
    3. Reflection across y=x
    4. Reflections across y=-x
  2. Translations
    1. Translations
  3. Rotations
    1. Rotating 90 degrees Clockwise
    2. Rotating 180 degrees about the origin
    3. Rotating 270 degrees clockwise about the orign

1.

Reflections

Explore reflections and their coordinate rules. Reflections across the x-axis, y-axis, y=x, and y= -x

  • 1. Reflecting across the x-axis
  • 2. Reflecting across the y-axis
  • 3. Reflection across y=x
  • 4. Reflections across y=-x

1.1.

Reflecting across the x-axis

Click and drag the blue dot. Observe it's reflection across the x-axis (the green dot). Pay attention to the coordinates from the blue dot to the green dot. How do they differ?
– akruizenga

1.2.

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1.3.

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1.4.

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2.

Translations

  • 1. Translations

2.1.

Translations

Click and drag the blue dot to translate the green dot according to the vector u. Pay attention to the coordinates. How do they relate to the coordinates of the green dot? How do they relate to the length of the vector?
– akruizenga

3.

Rotations

  • 1. Rotating 90 degrees Clockwise
  • 2. Rotating 180 degrees about the origin
  • 3. Rotating 270 degrees clockwise about the orign

3.1.

Rotating 90 degrees Clockwise

Click and drag the blue dot to see it's image after a 90 degree clockwise rotation (the green dot). Pay attention to the coordinates. How are they related?
– akruizenga

3.2.

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3.3.

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