1. TRANSFORMATIONS (CONTINUED)
Math Alliance January 25, 2011

2. Make a conjecture: What will happen if you transformB l A m n
Students will do it on the patty paper and then give a description of the outcome including how it compared to their conjecture.
The result is a translation, through a distance equal to twice the distance between the lines, and in the direction perpendicular to the lines and pointing from the first line to the second.
1 translation = 2 reflections
- What would have happened if you had done the two reflections in the opposite order?
Make a conjecture:
What will happen if you transform
ABC over n and then over m?

3. Make a conjecture: What will happen if you transformB A l m n
Students will do it on the patty paper and then give a description of the outcome including how it compared to their conjecture.
The result is a rotation. The point of rotation is the intersection of the perpendicular lines. Therefore the corresponding points of the figures are equidistant from the intersection of the perpendicular lines (the point of rotation).
1 rotation = 2 reflections
Make a conjecture:
What will happen if you transform
ABC over n and then over l?

4. Make a conjecture: What will happen if you reflectB A l n
Students will do it on the patty paper and then give a description of the outcome including how it compared to their conjecture.
Possible conjectures: A rotation? Why. A translation? Why. A reflection? Why.
Why can’t it be a glide reflection? (only 2 reflections. A glide reflection must be 3: 2 for the glide + 1 for the reflection)
Make a conjecture:
What will happen if you reflect
ABC over n and then over l?

5. Are there other possibilities?
Think about our previous discoveries.
Students will do it on the dot paper and then give a description of the outcome including how it compared to their conjecture.
- The distance between the parallel lines is fixed, however they can appear anywhere between the two original figures.
Given the translation, find two parallel lines such that successive reflections in the lines result in the given translation.
Are there other possibilities?