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Relative Distance Between Points

Relative Distance Between Points problems involve two persons or objects moving from the same or different starting points. You must calculate the straight-line distance between their final positions. These problems combine coordinate tracking for two entities with distance calculation.

10Worksheets
200+Practice Questions
HardDifficulty
2-3 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Relative Distance Between Points

Relative Distance Between Points problems involve two persons or objects moving from the same or different starting points. You must calculate the straight-line distance between their final positions. These problems combine coordinate tracking for two entities with distance calculation.

Prerequisites

Coordinate geometry Net displacement for multiple entities Distance formula Vector subtraction
Why This Matters: Relative Distance problems appear in 1-2 questions in advanced exams. They test multi-entity tracking and coordinate geometry.

How to Solve Relative Distance Between Points Problems

1

Step 1: Track coordinates for person A: (x_A, y_A)

2

Step 2: Track coordinates for person B: (x_B, y_B)

3

Step 3: Calculate differences: Δx = x_A - x_B, Δy = y_A - y_B

4

Step 4: Distance = √(Δx² + Δy²)

5

Step 5: If starting from same point, initial coordinates are (0,0) for both

6

Step 6: For different start points, account for initial positions

7

Step 7: Answer with the separation distance

Pro Strategy: Find final coordinates of each person independently. Then use the distance formula between those two points. The order of subtraction doesn't matter as squares make it positive.

Example Problem

Example: A walks 10 m East, 5 m North. B walks 6 m West, 8 m North from same start. Find distance between them. Solution: Step 1: A: (10,5) Step 2: B: (-6,8) Step 3: Δx = 10 - (-6) = 16, Δy = 5 - 8 = -3 Step 4: Distance = √(16² + (-3)²) = √(256 + 9) = √265 ≈ 16.28 m Answer: 16.28 m

Pro Tips & Tricks

  • Final position of A = (x_A, y_A)
  • Final position of B = (x_B, y_B)
  • Distance = √[(x_A - x_B)² + (y_A - y_B)²]
  • If starting from same point, initial positions cancel
  • The distance is independent of the order of subtraction

Shortcut Methods to Solve Faster

Calculate net displacement for each person
Use coordinate differences
Apply distance formula

Common Mistakes to Avoid

Subtracting coordinates in wrong order (order doesn't matter for squares)
Forgetting to square the differences
Adding coordinates instead of subtracting
Not accounting for different starting points

Exam Importance

Relative Distance Between Points is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
1-2 questions
BANKING PO
1-2 questions
RAILWAYS RRB
0-1 questions
CAT
1-2 questions
INSURANCE
1-2 questions

Ready to Master Relative Distance Between Points?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
Start Practicing Now