GATE 2025 BT – Question 10
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.
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Show answer and explanation
Correct answer: (B) Option B in the figure
Explanation
A cross with four arms is already 4-fold symmetric, so the dots decide it. Put the centre at the origin and the arms at distance 1.5. In B the dots are at the top-right corner of the top arm (0.5, 1.5), the bottom corner of the right arm (1.5, -0.5), the bottom-left corner of the bottom arm (-0.5, -1.5) and the top corner of the left arm (-1.5, 0.5). A $90^\circ$ clockwise turn takes each of these onto the next, so the figure is unchanged. In A, C and D the dots do not go onto each other under a quarter turn.