Reflectional Symmetry
The butterfly below has reflectional symmetry. The line of symmetry is the vertical line through the center of the butterfly, splitting it into two halves that are mirror images of one another. Use the construction to answer the following questions:
1) Move point B that lies on the line of symmetry. What do you notice about the distance of A and A' from the line of symmetry, regardless of where B is?
2) Move point A (you will see that it will leave a red, dotted path) to parts of the butterfly you think appear to be symmetric. How does each movement effect A'?
3) If you did not move point A across the line of symmetry, do so now. How does this effect A'?
After exploring the line of symmetry and implications for reflections, answer the following:
1) If you were to plot a segment with coordinates A(-2,3) and B(-2,7), what would segment A'B' if it was a reflection over the y-axis (the y-axis is the line of symmetry)?
2) If you were to draw a perpendicular line from point A to the y-axis, what is the distance A is from the y-axis? Without drawing A', what is the perpendicular distance A' is from the y-axis?