Single Vertical Fold - Basic
Single Vertical Fold problems involve folding a square paper vertically (left to right or right to left), then punching one or more holes through the folded layers. After unfolding, the holes appear in symmetric positions about the vertical fold line. These problems test your understanding of reflection symmetry across a vertical axis.
What You'll Learn
Introduction to Single Vertical Fold - Basic
Single Vertical Fold problems involve folding a square paper vertically (left to right or right to left), then punching one or more holes through the folded layers. After unfolding, the holes appear in symmetric positions about the vertical fold line. These problems test your understanding of reflection symmetry across a vertical axis.
Prerequisites
How to Solve Single Vertical Fold - Basic Problems
Step 1: Identify the fold direction - vertical fold means the paper is folded either left-to-right or right-to-left
Step 2: The fold line becomes the axis of symmetry - it runs vertically through 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 vertically from left to right. A hole is punched near the top-left of the folded paper at (30, 25). What is the pattern when unfolded? Solution: Step 1: Fold direction: vertical (left to right) Step 2: Fold line is at the vertical center (x = 50 on a 100x100 paper) Step 3: Hole position on folded paper: (30, 25) Step 4: When unfolded, the right layer hole stays at (30, 25) Step 5: The left layer hole mirrors across x=50: (30, 25) reflects to (70, 25) Step 6: Result: Two holes horizontally aligned at (30, 25) and (70, 25) Answer: Two holes horizontally aligned in the upper portion
Pro Tips & Tricks
- Vertical fold = horizontal symmetry in hole pattern (holes appear left and right of 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
- For 'left to right' fold, the left layer folds over the right layer
- For 'right to left' fold, the right layer folds over the left layer - symmetry is the same
- Mirror formula for vertical fold: x' = W - x (where W is paper width, x measured from left edge)
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Single Vertical 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: