Question

Which transformations map this strip pattern onto itself?

Geometric model
Group of answer choices

a horizontal translation and a 180° rotation

a horizontal translation and a reflection across a vertical line

a horizontal translation and a glide reflection

a horizontal translation only

Answer 1

I don’t have the picture, so I can’t choose for you. If you can upload the strip pattern (or describe a single repeating motif and how it’s oriented), I’ll pick the correct option.

If you want to decide it yourself, use these quick tests:

1. Confirm horizontal translation: find the smallest horizontal shift that carries one motif to the next. (All four answer choices include a horizontal translation.)

2. Test for a vertical reflection: pick a vertical line through a motif (or midway between two) and reflect. If the pattern falls exactly onto itself, a reflection across a vertical line is a symmetry.

3. Test for 180° rotation: pick a candidate center (often at motif centers or midpoints between motifs) and rotate the strip 180°. If everything matches, there is a 180° rotation symmetry.

4. Test for a glide reflection: reflect across a vertical line and then translate horizontally by half the repeat distance. If a single reflection fails but this combination maps the pattern onto itself, then you have a glide reflection.

Use these outcomes to choose:
- If you find vertical reflection (alone) → choose “a horizontal translation and a reflection across a vertical line.”
- If you find 180° rotation (but no reflection) → choose “a horizontal translation and a 180° rotation.”
- If you find only the reflect+half-translation but no plain reflection → choose “a horizontal translation and a glide reflection.”
- If none except translation → choose “a horizontal translation only.”

Send the image if you want me to identify the symmetry for you.