If possible, describe a geometric figure that can be transformed into itself by each of the following: Reflection, Rotation, Translation, Glide Reflection
To find a geometric figure that can be transformed into itself by each of the given transformations, let's consider a regular hexagon.
1. Reflection: A regular hexagon has six lines of reflection symmetry, passing through each pair of opposite vertices or through the midpoints of opposite sides. When a regular hexagon is reflected across any of these lines, it overlaps exactly with its original position.
2. Rotation: A regular hexagon can be rotated by 60 degrees (or multiples thereof) around its center, and it will coincide exactly with its original orientation. This is because the angle between each pair of consecutive vertices in a regular hexagon is always 120 degrees, which is divisible by 60.
3. Translation: A regular hexagon can be translated by any integral multiple of the side length, horizontally, vertically, or both, to coincide with its original position. This is because the shape and size of a regular hexagon remain the same, regardless of its position.
4. Glide Reflection: A glide reflection is a combination of a reflection and a translation. If we reflect a regular hexagon across one of its lines of symmetry, and then translate it by a vector that is parallel to that line, the hexagon will coincide exactly with its initial position.
Therefore, a regular hexagon is a geometric figure that can be transformed into itself by each of the given transformations: reflection, rotation, translation, and glide reflection.