Assume the following pattern continues in both directions. What isometries preserve the pattern?
A) translation and rotation only
B) translation and horizontal reflection only
C) translation, rotation, and vertical reflection only
D) translation, rotation, glide reflection, and vertical reflection

Question

Assume the following pattern continues in both directions. What isometries preserve the pattern? 
A) translation and rotation only 
B) translation and horizontal reflection only 
C) translation, rotation, and vertical reflection only 
D) translation, rotation, glide reflection, and vertical reflection

Quizplus · Accepted Answer

The pattern has both horizontal and vertical symmetry, so any isometry that preserves these symmetries can be used to preserve the pattern.
- Translation: Since the pattern continues indefinitely in both directions, translations can be used to shift the pattern without affecting its overall structure. 
- Rotation: The pattern has rotational symmetry around its center point, so rotations can be used to preserve the pattern. 
- Glide reflection: This isometry combines a translation with a reflection, so it can be used to both shift the pattern and reflect it across a line. The pattern exhibits glide symmetry along its horizontal axis, so glide reflections can be used to preserve the pattern. 
- Vertical reflection: The pattern also has vertical symmetry, so reflections across a vertical line can be used to preserve the pattern. 
Therefore, the best choice is D because it includes all four isometries that preserve the pattern.

Assume the Following Pattern Continues in Both Directions