Question

which transformations map the strip pattern onto itself?
ppppp
a horizontal translation only
a horizontal translation and a reflection across a vertical line
a horizontal translation and a glide reflection
a horizontal translation and a 180° rotation

Explanation:

1. Analyze horizontal translation: Shifting the pattern horizontally (e.g., moving each "P" to the position of the next "P") maps the pattern onto itself, as the pattern is repetitive horizontally.
2. Analyze reflection across vertical line: Reflecting a "P" over a vertical line would turn it into a mirror - image (like "q" or similar), which does not match the original "P" in the pattern, so reflection across vertical line does not map the pattern onto itself.
3. Analyze glide reflection: A glide reflection involves a translation and a reflection. Since reflection across vertical line doesn't work, glide reflection also doesn't work.
4. Analyze 180° rotation: Rotating a "P" 180° would change its orientation (it would look like an inverted "P" or a different character), which does not match the original pattern.
5. So only horizontal translation maps the strip pattern (of "PPPPP") onto itself.

Answer:

a horizontal translation only