Question 1
A transparent sheet is folded vertical (left to right). A single hole is punched at the upper section of folded paper. How will the paper look when unfolded?
Complete Solution with Visualization:
Step 1 - Paper Setup:
- Original shape: Square transparent sheet
- Fold type: vertical (left to right)
- Creates: 2 overlapping layers
- Orientation: Left half folds over right half
Step 2 - Fold Analysis:
- Vertical fold creates left-right symmetry
- Mirror axis runs vertically through center
- Left and right halves overlap perfectly
- Each point has a mirror counterpart
Step 3 - Punch Operation:
- Location: upper section of folded paper
- Punch penetrates: Both layers simultaneously
- Each layer receives identical hole at same position
- Hole appears in upper region of folded shape
Step 4 - Unfolding Process:
- Carefully unfold along the vertical crease
- The hole on the right half stays fixed
- The hole on the left half appears as mirror image
- Both holes maintain their vertical position
- Final pattern: Two holes horizontally aligned in the upper portion
Step 5 - Pattern Verification:
- Symmetry check: Holes mirror across vertical center line
- Layer count: 2 layers punched = 2 holes visible
- Alignment: Horizontal alignment at same y-coordinate
- Position: Both in upper portion of paper
- Correct answer: Two holes horizontally aligned in the upper portion
Spatial Reasoning Technique:
Use your finger to trace the fold line vertically. Imagine reflecting the punch point across this line - where your reflection lands is where the second hole appears.
Common Error: Students often confuse the fold direction with the hole alignment direction. Remember: vertical fold → horizontal hole alignment.
Coordinate Method: For hole at (x,y) in folded state, unfolded positions are (x,y) and (100-x,y) for 100x100 paper.