Given:
[tex]A_{GH}B_{GH}C_{GH}D_{_{GH}E_{GH}F_{GH}}[/tex]
is a reflected image of hexagon ABCD.
Line of reflection = GH.
Let's answer the following questions:
• Part A.
Drag the line of reflection until the image coincides with the preimage. What would happen if the preimage flips about the reflection line?
Here, we are given the midpoints in the preimage.
When the line GH is drag to coincide with the preimage, at this point if you flip the preimage about the line of reflection at this location, the reflection would map the ABCDEF back onto itself (here, the line of reflection would be at the midpoint of AB and DE).
Also, for the line to coincide, we are to drag the line to pass all midpoints(in this case the line will pass opposite midpoints), and all vertices of ABCDEF.
The green lines pass through the vertices of the hexagon. (3 green lines).
The red lines pass through the midpoints of the hexagon. (3 red lines).
Therefore, in total, we have 6 lines of GH that would map ABCDEF back onto itself.
ANSWER:
• Part A.
When the line GH coincides with the preimage, at this location if the preimage flips about the reflection line, it will map the hexagon back onto itself.
• Part B.
We can place line GH in six different positions so the image reflects onto the preimage in this manner.
