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 given figure consists of 16 unit squares arranged as shown. In addition to the three black squares, what is the minimum number of squares that must be coloured black, such that both PQ and MN form lines of symmetry? (The figure is representative)

• A. 3
• B. 4
• C. 5
• D. 6

Hint:

In problems involving symmetry, ensure each side of the line of symmetry mirrors the other. In grid-based questions, count squares symmetrically.

Answer 1

The Correct Option is C

To make PQ and MN lines of symmetry, the black squares must be placed symmetrically about these lines. The existing three black squares are placed on the given grid, and the task is to color the minimum number of additional squares to ensure symmetry along both PQ and MN lines.
By examining the figure, we find that a minimum of 5 additional squares need to be colored to ensure symmetry along both lines. Thus, the minimum number of squares to be colored is 5.