GATE CE 2025 Set 1 — Question 10
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General Aptitude → Spatial Aptitude → Transformation of Shapes (Translation, Rotation, Scaling, Mirroring)
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Question
An object is said to have an -fold rotational symmetry if the object, rotated by an angle of , 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.
Correct answer
(B) [figure]
Solution
4-fold rotational symmetry requires the object to look identical after a rotation of .In Option (B), the dots are placed as follows:
- Top arm: dot on the right side.
- Right arm: dot on the bottom side.
- Bottom arm: dot on the left side.
- Left arm: dot on the top side.
- The top arm moves to the right arm position, and its dot (right side) moves to the bottom side of the new position. This matches the original right arm.
- The right arm moves to the bottom arm position, and its dot (bottom side) moves to the left side. This matches the original bottom arm.
- The pattern continues for all arms, making the object identical to the original. Thus, (B) has 4-fold symmetry.
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