An object is said to have an n-fold rotational symmetry if the object, rotated…
2025
An object is said to have an n-fold rotational symmetry if the object, rotated by an angle of \(\frac{2\pi}{n}\), is identical to the original. Which one of the following objects exhibits 4-fold rotational symmetry about an axis perpendicular to the plane of the screen? Note: The figures shown are representative.
Answer: B. Figure B — A 4-fold symmetric object must coincide with itself after a rotation of \(\frac{2\pi}{4} = 90^\circ\) about the axis perpendicular to the screen. The…
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Figure A
- B.
Figure B
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Figure C
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Figure D
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Correct answer: B
A 4-fold symmetric object must coincide with itself after a rotation of \(\frac{2\pi}{4} = 90^\circ\) about the axis perpendicular to the screen. The cross-shaped outline alone repeats under every quarter-turn, so the marked dots decide the outcome: the whole figure is unchanged by the rotation only when each dot lands on a position occupied by another dot. In Figure B, a rotation of \(90^\circ\) carries every dot onto the position of another dot, so the rotated figure is indistinguishable from the original. Therefore Figure B exhibits 4-fold rotational symmetry.