Hexagon AGHBGHCGHDGHEGHFGH is a reflected image of hexagon ABCDEF. The midpoints of the sides of hexagon ABCDEF are also shown. Drag the line of reflection, until the image coincides with the preimage. At this location, if the preimage flips about the line of reflection, it will flip onto itself. In how many different positions can you place so the image reflects onto the preimage in this manner? Describe the different positions. Be sure to pass the line of reflection through both vertices and midpoints before answering.

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times both sides by 2, times () by 8, add alile terms, move terms, add alike and caculate divide both sides by 3

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1                     1

1                     2

1                     3

1                     4

2                   1

2                   2

2                   3

2                   4   = not 1, and 4

3                   1

3                   2

3                   3

3                   4 = not 1, and 4

only 2 outcomes have passed the given condition.

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