A square paper, shown in figure (I), is folded along the dotted lines as shown in figures (II) and (III). Then a few cuts are made as shown in figure (IV). Which one of the following patterns will be obtained when the paper is unfolded?
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When solving paper folding problems, carefully analyze the folds and cuts. Unfold the paper mentally to predict the resulting pattern by considering symmetry and the effects of the cuts.
To determine the pattern obtained when the square paper is unfolded, let us analyze the steps involved in the folding and cutting as shown in the given images.
Initial Position: The paper starts as a square, as shown in Figure (I).
First Fold: The square is folded along one of the diagonals to form a triangle, as seen in Figure (II).
Second Fold: The triangle is folded again along its altitude, resulting in a smaller right triangle, as shown in Figure (III).
Cutting: Certain sections are cut out from the folded paper, as depicted in Figure (IV).
When you unfold the paper after making the cuts, the pattern developed will have symmetry corresponding to the folds.
The correct pattern will mirror on each fold line. Therefore, when unfolded, the cuts made in the folded state will repeat on each quadrant of the square.
As inferred from the above steps, the pattern obtained should have the symmetry consistent with the folds along the diagonals. After considering all the options, the correct pattern is observed to be the one shown in the above image.
Thus, the pattern obtained when the paper is unfolded matches the correct option image presented.
