The numerals 1 - 13 in the annotated .png refer to the order in the construction recipe. Follow the recipe as far as time permits in the lab. You can store your .ggb file in the Moodle and retrieve it as long as you do not submit it. Submit your (annotated) .png to the Moodle during the lab or from home if you do not finish. The two files, the .ggb and the .png, submitted when requested, constitute the assignment.

Task

  1. Choose an arbitrary point A

  2. and point B

  4. Choose displacement vector D=B-A for the translation Make a "gnomon", which is any non-symmetric figure, and choose it to be translated. For instance the gamma shaped concave quadrilateral, or the fancier Start Man.

  5. Translate the gnomon a couple of times to see what repeated translation looks like. Then, wiggle B back an forth to see what the magnitude of the translation vector means. Wiggle B up and down to see what the direction of translation does.

  6. Choose an arbitrary point labelled X in the plane.

  7. Apply the translation to get X'. Note that GGB labels it X'.

  8. Construct the perpendicular bisector m for you first mirror.

  9. Reflect the blue starman across mirror m to get mirror image. (9b) Wiggle X and B to see their effect on the figure. Understand?

  10. Consruct the mirror n parallel to m through X'.

  11. Reflect purple starman through mirror n to grey starman. (11b) Wiggle X to see that although starman 9 moves with X, starman 11 does NOT! This should make you wonder why. Wiggle the original starman 5 to strengthen your suspicions.

  12. Give the third starman 5 a green flag to hold. Be sure you start at a point on his hand when you build the flag. STOP: Predict where the reflection in the second mirror, n, takes starman with flag.

  13. Were you right? Give yourself a 10 if you predicted correctly.