Reflection Over Oblique Lines
Explore Reflecting Over Two Oblique Lines
Introduction
In the diagram above, the polygon with segment AB has been reflected twice: first over line KL, then over line ML. You have seen something like this before: we have explored what happens when you reflect a figure over two parallel lines, and what happens when you reflect a figure over two perpendicular lines. In this activity, you will explore what happens when you reflect a figure over two oblique lines, that is, two lines that intersect at an angle that is not 90 degrees.
Question 1
Describe the transformation that represents the composition of the two reflections (from AB to A"B"). Be as specific as possible.
Explore
Experiment by clicking on and dragging the original polygon (with segment AB) to different locations on the window.
Question 2
How would you describe the effect that this has on the two reflection images of the original polygon?
Question 3
How would you describe the effect that moving the original polygon has on the angle ALA" ?
Explore
Now click on point K or point M and explore what happens as you change the angle at which the two lines intersect, making it wider or narrower. You can move point L as needed. You can also move the original polygon so that you can see better what is happening.
Question 4
How would you describe what happens to the reflection images as you change the size of the angle between the lines?
Question 5
How would you describe the relationship between ALA" and OLN ?
Sum it up:
After completing the activity, summarize in a complete sentence below the effect of reflecting a shape over two lines that intersect at an angle. "The effect of reflecting a figure over two oblique lines is...." Be as specific as possible.