Many rigid motions in geometry can be described by linear transformations. For instance, in R^{2} 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!]
Decide which of the following rigid motions can be described by a matrix transformation in R^{2}. 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