To create a wallpaper border using a tile, Carrie can apply various transformations to the left-most tile. Here’s a breakdown of the options provided:
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A horizontal translation: This would involve moving the tile left or right without altering its orientation. This transformation alone would not create a varied pattern.
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A rotation: This would turn the tile around a central point. While it could create interesting variations, it might not match the design needed for a continuous border.
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A reflection: This would flip the tile over a line, creating a mirror image. This transformation might be useful, but it often necessitates additional transformations for a complete border.
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A translation followed by a reflection: This combination would first move the tile to a new position, and then create a mirror image of the tile, which could effectively create the needed pattern for a wallpaper border.
Given these options, the best answer would depend on the specifics of the design of the wallpaper border. However, the option that often works well for creating diverse and symmetric patterns in wallpaper borders is:
A translation followed by a reflection.
This choice allows for the creation of a rich and varied pattern that can seamlessly wrap around the room.
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