Multi-Person Relative
Multi-Person Relative Position problems involve two or more persons moving from the same or different starting points. You must determine the relative position of one person with respect to another, including both direction and distance. These problems combine coordinate geometry with vector addition and relative displacement concepts.
What You'll Learn
Introduction to Multi-Person Relative
Multi-Person Relative Position problems involve two or more persons moving from the same or different starting points. You must determine the relative position of one person with respect to another, including both direction and distance. These problems combine coordinate geometry with vector addition and relative displacement concepts.
Prerequisites
How to Solve Multi-Person Relative Problems
Step 1: Assign coordinates to each person based on their movements from their starting points
Step 2: For each person, calculate final coordinates (x₁, y₁), (x₂, y₂), etc.
Step 3: To find position of person A relative to person B: (x_A - x_B, y_A - y_B)
Step 4: Calculate distance = √((x_A-x_B)² + (y_A-y_B)²)
Step 5: Determine direction based on the signs of (x_A-x_B) and (y_A-y_B)
Step 6: Express answer as direction and distance (e.g., '5 km North of B')
Step 7: Verify by drawing a diagram or using alternative method
Example Problem
Example: A walks 10 m East, then 5 m North. B walks 6 m West, then 8 m North from the same starting point. What is A's position relative to B? Solution: Step 1: A: (10, 5), B: (-6, 8) Step 2: A relative to B = (10 - (-6), 5 - 8) = (16, -3) Step 3: Distance = √(16² + (-3)²) = √(256 + 9) = √265 ≈ 16.28 m Step 4: x>0, y<0 → Southeast direction Answer: Approximately 16.28 m Southeast of B
Pro Tips & Tricks
- If both start from same point, subtract their coordinate differences
- If starting from different points, include starting coordinates in calculations
- Relative direction is from the reference person to the other person
- To find how B is from A, calculate (x_B - x_A, y_B - y_A)
- Use vector addition for complex multi-person scenarios
- Draw separate diagrams for each person's path if helpful
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Multi-Person Relative. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Multi-Person Relative is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Multi-Person Relative?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: