Single Horizontal Fold - Basic
Single Horizontal Fold problems involve folding a square paper horizontally (top to bottom or bottom to top), then punching one or more holes through the folded layers. After unfolding, the holes appear in symmetric positions about the horizontal fold line. These problems test your understanding of reflection symmetry across a horizontal axis.
What You'll Learn
Introduction to Single Horizontal Fold - Basic
Single Horizontal Fold problems involve folding a square paper horizontally (top to bottom or bottom to top), then punching one or more holes through the folded layers. After unfolding, the holes appear in symmetric positions about the horizontal fold line. These problems test your understanding of reflection symmetry across a horizontal axis.
Prerequisites
How to Solve Single Horizontal Fold - Basic Problems
Step 1: Identify the fold direction - horizontal fold means the paper is folded either top-to-bottom or bottom-to-top
Step 2: The fold line becomes the axis of symmetry - it runs horizontally across the center
Step 3: Note the hole position(s) on the folded paper
Step 4: When unfolded, each hole creates a mirror image across the fold line
Step 5: A single hole punched through 2 layers creates 2 holes in the unfolded paper
Step 6: The distance of each hole from the fold line remains the same on both sides
Step 7: Combine the original hole positions with their reflections to get the final pattern
Example Problem
Example: A square paper is folded horizontally from top to bottom. A hole is punched at the center of the folded paper. What is the pattern when unfolded? Solution: Step 1: Fold direction: horizontal (top to bottom) Step 2: Fold line is at the horizontal center (y = 50 on a 100x100 paper) Step 3: Hole position on folded paper: center (50, 50) Step 4: When unfolded, the top layer hole stays at (50, 50) Step 5: The bottom layer hole mirrors across y=50: (50, 50) reflects to (50, 50) - same point! Step 6: Actually, punching at the exact center creates a single hole at center (both layers align) Step 7: If hole was at (50, 30), mirror would be at (50, 70) → two holes vertically aligned Answer: One hole at the center (if punched exactly at center) or two vertically aligned holes
Pro Tips & Tricks
- Horizontal fold = vertical symmetry in hole pattern (holes appear above and below the fold line)
- The distance from the fold line remains constant for mirrored holes
- If a hole is exactly on the fold line, it creates only ONE hole when unfolded (both layers align)
- For 'top to bottom' fold, the top layer folds over the bottom layer
- For 'bottom to top' fold, the bottom layer folds over the top layer - symmetry is the same
- The number of holes after unfolding = Number of layers × Number of punches (unless overlapping)
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Single Horizontal Fold - Basic. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
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Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: