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Linear Transformations

Part 4: Matrix Transformations and Rigid Motions

  1. Many rigid motions in geometry can be described by linear transformations. For instance, in R2 reflection across the horizontal axis is a rigid motion that can be represented by a matrix. What is the relevant matrix? [Hint: You saw this transformation in Part 3!]
  2. Decide which of the following rigid motions can be described by a matrix transformation in R2. For motions that are linear transformations, give an example of a matrix that could define such a transformation. For motions that are not linear transformations, say which property of linear transformations is not satisfied.
    • Reflection across the vertical axis
    • Counter-clockwise rotation through an angle theta
    • Translation to the right r units and upward u units
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