GATE CS 2024 Set 1 | Question 10

MCQ · 2 marks · −0.66

The least number of squares to be added in the figure to make AB a line of symmetry is

A horizontal dashed line runs from A on the left to B on the right. Left group: one square sits on top of the line, one square hangs just below the line to its lower left, and one square sits two rows below the line directly under the top square, with the cell directly under the top square left empty; right group: three squares hang below the line in an L shape, two side by side touching the line and one beneath the right-hand square.
  1. Option A: 6 (correct)
  2. Option B: 4
  3. Option C: 5
  4. Option D: 7

Answer

(A)

Explanation

For AB to be a line of symmetry, every square needs a mirror image on the other side of AB, at the same distance from the line.

  • Left group: the square above the line needs its image in the empty cell directly below it; the square just below the line on the left needs an image just above the line; the square two rows down needs an image two rows up. That is 3 squares.
  • Right group: all three squares lie below the line, so each needs an image above it: 3 more squares.

None of these six cells is already filled, so the least number is \(3 + 3 = 6\).

Answer: A