GATE CE 2023 Set 1 — Question 5

MCQ+1 / -0.33MediumTransformation of Shapes (Translation, Rotation, Scaling, Mirroring)Spatial AptitudeGeneral Aptitude2D & 3D Patterns

General Aptitude → Spatial Aptitude → 2D & 3D Patterns

Last updated 5 September 2026

Question

A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line. The figure below consists of 20 unit squares arranged as shown. In addition to the given black squares, upto 5 more may be coloured black. Which one among the following options depicts the minimum number of boxes that must be coloured black to achieve two lines of symmetry? (The figure is representative)

Correct answer (B) c, d, i Solution To achieve two lines of symmetry (horizontal and vertical), the pattern must be symmetric about both axes. 1. Vertical Symmetry (between columns 2 and 3): The square 'i' at (4,2) must be black to match the black square at (4,3). 2. Horizontal Symmetry (about row 3): The square 'd' at (2,3) must be black to match the black square at (4,3). The square 'c' at (2,2) must be black to match square 'i' at (4,2) (which we already determined must be black). Thus, coloring c, d, and i black is the minimum requirement to satisfy both symmetries. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

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Correct answer (B) c, d, i Solution To achieve two lines of symmetry (horizontal and vertical), the pattern must be symmetric about both axes. 1. Vertical Symmetry (between columns 2 and 3): The square 'i' at (4,2) must be black to match the black square at (4,3). 2. Horizontal Symmetry (about row 3): The square 'd' at (2,3) must be black to match the black square at (4,3). The square 'c' at (2,2) must be black to match square 'i' at (4,2) (which we already determined must be black). Thus, coloring c, d, and i black is the minimum requirement to satisfy both symmetries.

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