Final answer:
The strip pattern 'PPPPP' can map onto itself with either a horizontal translation or a glide reflection.
A horizontal translation maintains the pattern as it slides across, and a glide reflection that includes a horizontal translation will also keep the pattern identical.
Therefore, the correct answer is: option "a horizontal translation and a glide reflection".
Step-by-step explanation:
When we say a pattern maps onto itself, we mean that after the transformation is applied, the pattern looks exactly as it did before the transformation.
For a horizontal strip pattern like the one given, a horizontal translation moves the strip left or right, and the pattern remains unchanged because it has translational symmetry along the horizontal axis.
Therefore, a horizontal translation would map the pattern onto itself.
In contrast, a 180° rotation around a central point would not map the strip pattern onto itself because it would flip the pattern upside down, which would only work if the pattern were symmetric about that central point in both the horizontal and vertical orientations.
Similarly, a reflection across a vertical line changes the left-to-right order of elements in the pattern, which, for a non-symmetric pattern like this one, would make it look different.
Lastly, a glide reflection combines a reflection in a line and a translation parallel to that line. For this strip pattern, if the reflection is perpendicular to the strip and the translation is along the length of the strip, the pattern would indeed map onto itself because the horizontal aspect of the pattern remains consistent.