Question

which transformation will carry a regular hexagon onto itself select all that apply a reflection across a line through the midpoints of opposite sides a rotation of 60 about the center a rotation of 240 about the center a translation 1 unit to the right a reflection across a line through opposite vertices a reflection across a line that connects nonadjacent vertices a rotation of 72 about the center

Answer 1

Select these four:

- Reflection across a line through the midpoints of opposite sides — yes (there are 3 such reflection axes).
- Rotation of 60° about the center — yes (rotations by multiples of 60° are symmetries).
- Rotation of 240° about the center — yes (240° = 4·60°, a multiple of 60°).
- Reflection across a line through opposite vertices — yes (there are 3 such axes).

Do not select: translation 1 unit to the right (moves the hexagon), reflection across a line connecting nonadjacent vertices that is not an opposite-vertex axis (such a line does not go through the center so is not a symmetry), or rotation of 72° (not a multiple of 60°).