Question

1. what transformation is used to create this frieze pattern?

glide reflection
vertical reflection
180° rotation
horizontal reflection

Explanation:

A glide reflection is a combination of a translation (sliding) and a reflection. In a frieze pattern, if the pattern is moved (translated) and then reflected (either over a vertical or horizontal line in the direction of the translation), it is a glide - reflection.
A vertical reflection would flip the pattern over a vertical line. But in a frieze pattern created by vertical reflection, the pattern would be symmetric about vertical lines between the motifs. However, for a glide - reflection, the reflection is combined with a translation.
A \(180^{\circ}\) rotation would turn the pattern \(180^{\circ}\) around a point. But in the given frieze pattern, the orientation of the triangles (for example, the tip of the triangle is in the same direction in a non - rotated sense when considering the overall pattern generation) does not suggest a \(180^{\circ}\) rotation.
A horizontal reflection would flip the pattern over a horizontal line. But the given frieze pattern is not symmetric about a horizontal line in the sense of just reflection; it has a translational component along with reflection.

Answer:

glide reflection