Question

Which transformations map the strip pattern onto itself? Geometric Model

a) Rotation and Reflection
b) Glide Reflection and Vertical Translation
c) Horizontal Translation and Rotation
d) Vertical Reflection and Half-turn

Answer 1

Horizontal translation and half-turn rotation are transformations that can map a strip pattern onto itself because they preserve the pattern's repeating nature and alignment.

Step-by-step explanation:

To determine which transformations map the strip pattern onto itself, we must consider the geometry of the pattern and the types of transformations that can be applied. A strip pattern typically repeats itself in a specific direction, which makes certain transformations like translations and rotations more likely to map the pattern onto itself. In some cases, reflections can also work, depending on how the pattern is oriented. Among the options provided, if a strip has a repeating pattern along its length, a horizontal translation (option c) would move the strip along its length, matching it onto itself. A half-turn rotation, which is a 180-degree rotation, would also map the pattern onto itself since the repeated elements would align after the turn.