GATE CS 2024 Set 1 — Question 10
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumTransformation of Shapes (Translation, Rotation, Scaling, Mirroring)Spatial AptitudeGeneral Aptitude
General Aptitude → Spatial Aptitude → Transformation of Shapes (Translation, Rotation, Scaling, Mirroring)
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Question
The least number of squares to be added in the figure to make AB a line of symmetry is
Correct answer
(A) 6
Solution
To make the line AB a line of symmetry, every shaded square on one side of the line must have a corresponding shaded square on the other side at the same distance from the line.Let's analyze the positions of the existing squares relative to the line AB:
1.Above the line:
- One square at column 3, 2 units above.
- One square at column 4, 1 unit above.
- One square at column 2, 1 unit below.
- One square at column 4, 1 unit below.
- A block of squares at columns 5 and 6, spanning 1 and 2 units below (total 4 squares).
- The square at (column 4, 1 unit above) and the square at (column 4, 1 unit below) are already symmetric to each other. No squares need to be added here.
- The square at (column 3, 2 units above) needs a reflection at (column 3, 2 units below). (+1 square)
- The square at (column 2, 1 unit below) needs a reflection at (column 2, 1 unit above). (+1 square)
- The block at (columns 5-6, 1-2 units below) needs a reflection at (columns 5-6, 1-2 units above). (+4 squares)
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