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12-53.
  1. Find the images of the four points , , , and by the matrix .


  2. Graph these points.

  3. What is the image of the square whose vertices are the points , , , and ? Shade it on the graph you made in part (b).

  4. What is the name of this geometric figure?

  5. Sketch the images of the lines , , and .

For the line , all points are of the form .

Hence and .
Write an equation relating x and y.

If you graphed the original line and its image, how would it relate to the original square and its image in parts (a) and (b)?