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Straight Line Distance

Straight Line Distance problems involve calculating the shortest distance (displacement) between a starting point and ending point after a person walks in multiple directions (North, South, East, West). These problems test your ability to track net displacement and apply the Pythagorean theorem to find the straight-line distance.

10Worksheets
200+Practice Questions
BeginnerDifficulty
1-2 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 Straight Line Distance

Straight Line Distance problems involve calculating the shortest distance (displacement) between a starting point and ending point after a person walks in multiple directions (North, South, East, West). These problems test your ability to track net displacement and apply the Pythagorean theorem to find the straight-line distance.

Prerequisites

Understanding of cardinal directions Coordinate geometry basics Pythagorean theorem Net displacement calculation
Why This Matters: Straight Line Distance problems are fundamental to distance logic. You can expect 2-3 questions in SSC CGL, 2-3 in Banking PO, and 2-3 in Railways RRB exams.

How to Solve Straight Line Distance Problems

1

Step 1: Assign coordinates: starting point as (0,0)

2

Step 2: For each movement, update coordinates: North (+y), South (-y), East (+x), West (-x)

3

Step 3: Calculate net displacement in x and y directions

4

Step 4: Apply Pythagorean theorem: Distance = √(x² + y²)

5

Step 5: Round to nearest integer or as required

6

Step 6: Answer with the distance and direction if asked

Pro Strategy: Always track net East-West and North-South separately. The straight-line distance is the hypotenuse of the right triangle formed by net displacements.

Example Problem

Example: A person walks 10 m East, then 5 m North, then 10 m West. What is his straight line distance from start? Solution: Step 1: Start (0,0) Step 2: 10 m East → (10,0) Step 3: 5 m North → (10,5) Step 4: 10 m West → (0,5) Step 5: Net displacement = (0,5) Step 6: Distance = √(0² + 5²) = 5 m Answer: 5 m

Pro Tips & Tricks

  • Net East-West = Σ(East distances) - Σ(West distances)
  • Net North-South = Σ(North distances) - Σ(South distances)
  • Distance = √(EW² + NS²)
  • If net displacement is zero, the person returns to start
  • Draw a diagram for complex movements
  • Pythagorean triplets (3-4-5, 5-12-13) help quick calculation

Shortcut Methods to Solve Faster

Distance = √(x² + y²) where x = net EW, y = net NS
Total path length = sum of all distances walked
Displacement is always ≤ total path length

Common Mistakes to Avoid

Adding distances instead of calculating net displacement
Forgetting to use signs for opposite directions
Not using Pythagorean theorem for non-collinear movements

Exam Importance

Straight Line Distance is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
2-3 questions
BANKING PO
2-3 questions
RAILWAYS RRB
2-3 questions
CAT
1-2 questions
INSURANCE
2-3 questions

Ready to Master Straight Line Distance?

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

20 practice questions
Detailed solutions
Step-by-step explanations
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