Transformations

Transformations

1. Reflection

   • See Reflection FlashCards
     • Rigid Transformation: Reflection Review
   • Rules
     • Reflect Across X-Axis
       • (x, y) ----> (x, -y)
     • Reflect Across Y = X
       • (x, y) ----> (y, x)
     • Reflect Across Y-Axis
       • (x, y) ----> (-x, y)
     • Reflect Across X = Number
       • (x, y) ----> (x, 0+(coordinate to the number)*2)
         • *If the coordinate > number, y is negative.*
     • Reflect Across Y = -X
       • (x, y) ----> (-y, -x)
     • Reflect Across Y = Number
       • (x, y) ----> ( 0+(coordinate to the number)*2 , y)
         • *If the coordinate > number, x is negative.*
     • Reflect Across the Orgin
       • (x, y) ----> (-y, -x)
   • A reflection is the image of a figure that has been “flipped” over a line of reflection. A reflection is also a rigid transformation which means the preimage and image are congruent.
   • The preimage is always the same distance away from the line of reflection as the image.

2. Translation

   • Translation: the process of moving something from one place to another.
   • Examples:
     • Step 1: (x + 3, y + 2) Step 2: (x - 2, y + 5)
       • Result: (x, y) ----> (x - 1, y + 7)
     • Step 1: (x - 10, y + 10) Step 2: (x - 10, y + 10)
       • Result: (x, y) ----> (x - 20, y + 20)
     • Step 1: (x + 3, y + 2) Step 2: (x - 3, y - 2)
       • Result: (x, y) ----> (x, y)
     • Step 1: (x + 5, y + n) Step 2: (x - n, y + 7)
       • Result: (x, y) ----> (x + 5 - n, y + 7 + n)

3. Dilation

   • A dilation is a transformation (notation ) that produces an image that is the same shape as the original, but is a different size. A dilation stretches or shrinks the original figure. The description of a dilation includes the scale factor (or ratio) and the center of the dilation.
   • See Transformation Flashcards (Edit on Jadéjah Robinson's work)
     • Transformation Flashcards

4. Rotation

   • A rotation is a transformation which is also called a “turn”. A rotation uses a point as its center of rotation. This center of rotation may or may not be on the figure. A rotation is a rigid transformation, which means the preimage and image are congruent.

5. There are Two types of transformations, one is Rigid Transformation, and one is Non-Rigid Transformation

   • Rigid Transformation is a transformation of a figure that preserves size and shape. The three kinds of rigid transformations studied are translation (slide), reflection (flip), and rotation (turn).
   • Non-rigid transformations change the size but not the shape of the preimage, dilation is a non-rigid transformation
   • Take the quiz if you are ready
     • Transformation

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