Combined Rotation-Scaling Analogy
Combined Rotation-Scaling Figure Analogy problems involve two or more transformations applied in sequence. Common combinations include rotation followed by scaling, or scaling followed by rotation. You must identify both transformations and apply them to a new figure. These problems test advanced spatial reasoning and multi-step transformation skills.
What You'll Learn
Introduction to Combined Rotation-Scaling Analogy
Combined Rotation-Scaling Figure Analogy problems involve two or more transformations applied in sequence. Common combinations include rotation followed by scaling, or scaling followed by rotation. You must identify both transformations and apply them to a new figure. These problems test advanced spatial reasoning and multi-step transformation skills.
Prerequisites
How to Solve Combined Rotation-Scaling Analogy Problems
Step 1: Analyze the transformation from Figure A to Figure B
Step 2: Identify if rotation and scaling are both present
Step 3: Determine the rotation angle (90°, 180°, 270°) and direction
Step 4: Determine the scaling factor (enlargement or reduction)
Step 5: Apply the rotation to Figure C first, then scaling (order matters)
Step 6: Alternatively, apply scaling then rotation (commutative if both are linear)
Step 7: The correct answer is the transformed Figure C
Example Problem
Example: Figure A: small triangle pointing right. Figure B: larger triangle pointing up (90° anticlockwise + 1.5× scaling). Figure C: small horizontal rectangle. What should Figure ? look like? Solution: Step 1: A→B: rotation 90° anticlockwise + scale 1.5× Step 2: Apply to C: horizontal rectangle Step 3: Rotate 90° anticlockwise → vertical rectangle Step 4: Scale 1.5× → larger vertical rectangle Step 5: Answer: Larger vertical rectangle Answer: Vertical rectangle enlarged 1.5×
Pro Tips & Tricks
- Rotation changes orientation, scaling changes size
- Order of operations matters: rotate then scale vs scale then rotate
- If both transformations are present, both must be applied to C
- Check if the transformations commute (they do for rotation and scaling about the same center)
- Common combinations: 90° rotation + 2× scaling, 180° rotation + 0.5× scaling
- The scaling factor may be whole number or fraction
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Combined Rotation-Scaling Analogy. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Combined Rotation-Scaling Analogy is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Combined Rotation-Scaling Analogy?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: