Problem 22 · 2018 Math Kangaroo
Stretch
Spatial & Visual Reasoning
reflectiontransformations
A decorated glass tile is mirrored several times along the boldly printed edge. The first mirror image is shown. What does the tile on the far right look like after the third reflection?
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Answer: B
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Hint 1 of 3
Picture the tile as a stamp pressed over and over: each mirror across the next bold edge flips it left-to-right, like turning the page of a book.
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Hint 2 of 3
Think about whether the tile faces the same way or the flipped way after 1 flip, after 2 flips, after 3 flips.
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Hint 3 of 3
One flip and three flips leave it mirror-flipped; two flips bring it back to looking like the original.
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Approach: track that each flip mirrors the tile, so an odd number of flips gives a mirror image of the start
- Each reflection across a bold edge flips the tile left-to-right, so after one flip the picture is the mirror image of the original.
- A second flip turns it back to the original look, and a third flip makes it the mirror image again — so after three flips the tile is the mirror image of the starting tile.
- The picture that is the left-right mirror of the original tile is B, the answer.
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