The sequence of folding a paper and the manner in which the folded paper is cut is shown in the following figures. How would this paper look when unfolded?
Correct Answer :
Solution :
To determine how the paper will look when unfolded, we can analyze the folding and cutting process step-by-step using spatial symmetry and mirror reflections.
Step 1: Understand the folding steps
1. First Fold: The original rectangular sheet of paper is folded vertically in half from right to left. The vertical middle line acts as the fold line.
2. Second Fold: The paper is then folded horizontally in half from top to bottom. The horizontal middle line acts as the fold line.
After these two folds, the remaining visible portion of the paper is the bottom-left quadrant.
Step 2: Analyze the cuts on the folded quadrant
Let us examine the final folded figure:
- Near the top edge of this quadrant (which lies along the horizontal center line of the full page), there is a cut in the shape of a cross. The vertical bar of this cross is positioned slightly to the left of the horizontal bar's center.
- In the bottom-left corner, there is a thick diagonal cut line running from top-left to bottom-right, a thin parallel diagonal cut line to its left (closer to the corner), a small dot in the corner itself, and a small dot to the right of the thick diagonal line.
Step 3: Unfold step-by-step using symmetry
1. Unfold Vertically (from bottom to top):
- We reflect the bottom-left quadrant across its top edge (the horizontal center line) to get the top-left quadrant.
- The cross shape reflects vertically, appearing just above the horizontal center line, with the vertical bar still positioned on the left side of the cross.
- The diagonal lines and dots at the bottom-left corner reflect to the top-left corner. In this reflection, the diagonal lines now slope from bottom-left to top-right. The dots are positioned at the top-left corner and near the top-center line.
2. Unfold Horizontally (from left to right):
- We reflect the entire left half (both the top-left and bottom-left quadrants) across the vertical center line to complete the right half of the sheet.
- The crosses near the horizontal center on the left reflect to the right, where the vertical bar of the crosses will be on the right side of the cross.
- The diagonal cut lines and dots at the left corners reflect to the right corners, creating a symmetrical design on all four corners of the sheet.
Comparing our unfolded pattern with the options, it matches the design shown in the first option:
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