Set 1: Mirror reflections

1. Create two points and label them A and B.
2. Create a line on points A and B and label the line L.
   • Move A and watch L move, pivoting on the point B.
   • "Grab" L at a point distinct from both A and B, and watch L move. What happens ot A and B?
3. Create a point P not on L.
4. Construct the mirror image (reflection) of P in the line L and label it P'
   • Move P and verify that P' responds appropriately.
5. Create and label two points S and T (both not on L).
6. Create the segment with end points S and T.
7. Construct the reflection of segment in L
8. Label the end points of the reflection S' and T'.
   • Verify that the reflection of the segment is working correctly:
     1. by moving S,
     2. by moving T,
     3. by moving the segment ST itself by grabbing it at an interior point.
9. Create two points U and V,
10. Create the line M on U and V.
11. Construct the reflection of M in L. Label it M'.
12. The reflections of U and V do not appear.
    • Verify the movements of and M' three ways, just as you did with the segment ST, above.
13. Create a circle C by its center and it radius.
14. Construct a point X on C.
15. Find X', the reflection of X in L.
    • Use the locus feature of GeoGebra to find the locus of X' as a function of X.
    • Notice how X and X' traverse their paths in opposite direction: one clockwise, the other counter-clockwise.
    • Notice what happens when you "grab" the centre of your circle and move it about. Does the radius of the circle change?
    • Notice what happens when you "grab" a point on the circle and move it about.
16. Verify to your own satisfaction that each of your constructions is doing the right thing.
    1. Move the line L by "grabbing" it at a point disttinct from both A and B and watch L move to positions parallel to itself, but more importantly, see that all of the reflections you created all move together in the same direction and at the same speed.
    2. Change the slope of line L by moving the point B about. See L turn on the point A, but more imprtantly, see how how all the points and other objects you created move along circular arcs with center at A.
    3. Question 1. There is something deep here about translations and about rotations. Try to express this as best you can.
17. Save your work. Print a copy of your figure.
18. Use the "View" tab in the menu bar to view the "Construction Protocol." Print the "Construction Protocol."
19. Submit your Figure, the Construction Protocol, and your answer to Question 1. Deposit your solution in the drop box before the beginning of class on Friday, the 14th.
20. Inner workings, for your own edification. Make a copy your saved file, and for this copy, change the extender from .GGB to .ZIP. Unzip this file to view the inner structure of what you created. Do not hand this in.