Diagonal Fold - Basic
Diagonal Fold problems involve folding a square paper along one of its diagonals (top-left to bottom-right or top-right to bottom-left), then punching holes through the folded layers. After unfolding, the holes appear in symmetric positions about the diagonal fold line. These problems test your ability to visualize reflection across a 45° axis.
What You'll Learn
Introduction to Diagonal Fold - Basic
Diagonal Fold problems involve folding a square paper along one of its diagonals (top-left to bottom-right or top-right to bottom-left), then punching holes through the folded layers. After unfolding, the holes appear in symmetric positions about the diagonal fold line. These problems test your ability to visualize reflection across a 45° axis.
Prerequisites
How to Solve Diagonal Fold - Basic Problems
Step 1: Identify which diagonal is the fold line (top-left to bottom-right, or top-right to bottom-left)
Step 2: The diagonal becomes the axis of symmetry
Step 3: For top-left to bottom-right diagonal, the reflection rule is: (x, y) → (y, x)
Step 4: For top-right to bottom-left diagonal, the reflection rule is: (x, y) → (W - y, W - x)
Step 5: Note the hole position(s) on the folded paper
Step 6: Apply the reflection rule to find mirrored hole positions
Step 7: Combine original and mirrored holes to get the final pattern
Example Problem
Example: A square paper is folded diagonally from top-left to bottom-right. A hole is punched at (35, 55). Find the unfolded hole pattern. Solution: Step 1: Fold diagonal: top-left (0,0) to bottom-right (100,100) Step 2: Reflection rule: (x, y) → (y, x) Step 3: Original hole: (35, 55) Step 4: Mirrored hole: (55, 35) Step 5: Both holes are in the upper half of the paper Step 6: Result: Two holes diagonally symmetric across the main diagonal Answer: Two holes at (35, 55) and (55, 35) - symmetric about the diagonal
Pro Tips & Tricks
- Diagonal from top-left to bottom-right: reflection swaps x and y coordinates
- Diagonal from top-right to bottom-left: reflection sends (x,y) to (W-y, W-x)
- The sum of coordinates is constant for anti-diagonal reflection: x + y = constant
- Holes appear symmetrically on either side of the diagonal fold line
- If a hole lies exactly on the diagonal, it creates only ONE hole when unfolded
- The distance from the diagonal remains constant for mirrored holes
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Diagonal 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: