Introduction To Transformations

🔑 Key Concepts

  • A transformation moves or changes a figure to create a new figure.
  • Translations, reflections, and rotations are rigid transformations because they preserve size and shape.
  • A dilation is usually a non-rigid transformation because it changes the size of the figure.
  • The original figure is called the preimage, and the transformed figure is called the image.
  • Prime notation, such as \(A'\), \(B'\), and \(C'\), is used to name the image points after a transformation.

✏️ Worked Examples

🧠 Math Vocabulary

  • Transformation: A movement or change that maps a figure to a new figure.
  • Preimage: The original figure before a transformation.
  • Image: The new figure after a transformation.
  • Prime notation: Symbols such as \(A'\), \(B'\), and \(C'\) used to name image points. A second transformation may use double prime notation, such as \(A''\).
  • Rigid transformation: A transformation that preserves distance and angle measure. Translations, reflections, and rotations are rigid transformations.
  • Non-rigid transformation: A transformation that changes the size or shape of a figure.
  • Translation: A slide that moves every point the same distance in the same direction.
  • Reflection: A flip across a line of reflection.
  • Rotation: A turn around a center of rotation.
  • Dilation: A transformation that resizes a figure using a scale factor.
  • Scale factor: The multiplier used to enlarge or reduce a figure during a dilation.
  • Center of rotation: The fixed point around which a figure turns.
  • Center of dilation: The fixed point from which a figure is enlarged or reduced.
  • Origin: The point \((0,0)\) on the coordinate plane.
  • Congruent figures: Figures with the same size and same shape.
  • Similar figures: Figures with the same shape but not necessarily the same size.

💡 Main Idea

Transformations describe how figures move or change. Translations, reflections, and rotations are rigid transformations because the image is congruent to the preimage. Dilations are non-rigid transformations when the scale factor changes the size of the figure.

📚 What You Should Already Know

Students should know how to recognize basic shapes, compare size and shape, use the coordinate plane, and understand that congruent figures have the same size and shape.

🚀 What Comes Next

Students can move from identifying transformations to applying coordinate rules, graphing image points, describing sequences of transformations, and comparing congruence and similarity.

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