Final answer:
The translation that produces symmetry for the given pattern extended horizontally is D) Translation both to the right and left, as this allows for a seamless and symmetrical continuation of the pattern in both directions.
Step-by-step explanation:
To determine which translation produces symmetry for the given pattern when extended horizontally forever, we need to understand that symmetry in this context implies that the pattern can be translated (or slid) in a certain direction and still align perfectly with itself. This means the shapes, when moved a specific distance in a particular direction, match up at every point without altering their orientation.Considering the options provided, for a pattern to be symmetric when extended horizontally, it must be able to be translated in both right and left directions on a horizontal line. This is analogous to having a bilaterally symmetric organism, which, when split down the middle, results in two equal halves that are mirror images of each other. Translating such a pattern to the right or left should result in the pattern continuing seamlessly.
The direct answer to the question is D) Translation both to the right and left. This option ensures that the pattern, if reflected on either side, would align with its continuation, maintaining the symmetry along the horizontal direction. This concept is shown by the fact that bilaterally symmetric organisms can be split down their longitudinal axis to produce two equal halves, which is similar to extending a pattern horizontally and having it line up perfectly on both sides with its mirrored self.