CHAPTER 16 – PROBLEMS FOR WRITING AND DISCUSSION

  1. Chungsim has taken an L-shaped figure and reflected it over a line, p. She then took the image and reflected that over a second line, q. The two lines meet in a 40° angle at point F. Chungsim asks you, "Did I have to do two motions? Could I have done it with just one flip?" How would you respond? Be specific.
  1. A student claims that SO,5 is the same asSO,2followed bySO,3. By constructing an example, explain whether or not the students conclusion is correct.
  2. Draw a triangle on a piece of paper and label it . Now draw two distinct points, P and Q, somewhere on the page so that and can each be constructed. Label the image of as and the image of as . Describe the differences and similarities between the two resulting images.
  3. Suppose a figure on a coordinate grid is reflected over the x-axis and that image is then reflected over the y-axis. Describe a single transformation that would map the original figure to the final image.
  4. A rotation is defined according to its center and angle of rotation. If the center of a rotation were moved, how would that affect the resulting images of the transformed figures? Discuss what attributes of the image would change and what would remain the same. Some attributes to consider are size, shape, orientation, and location on the plane.
  5. A reflection is defined by the line of reflection. If the line of reflection were moved, how would that affect the resulting images of the transformed figures? Discuss what attributes of the image would change and what would remain the same. Some attributes to consider are size, shape, orientation, and location on the plane.
  6. A translation is defined by a directed line segment. If the directed line segment were moved, how would that affect the resulting images of the transformed figures? Discuss what attributes of the image would change and what would remain the same. Some attributes to consider are size, shape, orientation, and location on the plane.