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Shortest Distance

Shortest Distance problems involve a person walking in multiple directions (North, South, East, West) and you must find the straight-line distance between the starting and ending points. These problems use the Pythagorean theorem to calculate displacement from net East-West and North-South movements.

10Worksheets
200+Practice Questions
IntermediateDifficulty
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 Shortest Distance

Shortest Distance problems involve a person walking in multiple directions (North, South, East, West) and you must find the straight-line distance between the starting and ending points. These problems use the Pythagorean theorem to calculate displacement from net East-West and North-South movements.

Prerequisites

Basic direction sense Net displacement calculation Pythagoras theorem (a² + b² = c²) Square root calculation Coordinate geometry basics
Why This Matters: Shortest Distance problems appear in 2-3 questions in SSC CGL and Banking PO exams. They test application of Pythagoras theorem in direction sense contexts.

How to Solve Shortest Distance Problems

1

Step 1: Break each movement into its East-West and North-South components

2

Step 2: Calculate net East-West displacement (East = +, West = -)

3

Step 3: Calculate net North-South displacement (North = +, South = -)

4

Step 4: Use Pythagoras theorem: Distance = √(EW² + NS²)

5

Step 5: Round the answer to required decimal places

6

Step 6: If net displacement is zero, answer is 0 (returned to start)

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Step 7: Present the distance with appropriate units (meters, km, etc.)

Pro Strategy: Always calculate net East-West and net North-South separately. Treat East as positive, West as negative; North as positive, South as negative. Apply Pythagoras theorem to find straight-line distance.

Example Problem

Example: A person walks 3 km East, then 4 km North. What is the shortest distance from start to finish? Solution: Step 1: East-West: +3 km Step 2: North-South: +4 km Step 3: Distance = √(3² + 4²) = √(9 + 16) = √25 = 5 km Answer: 5 km

Pro Tips & Tricks

  • Draw a rough diagram showing the path and the direct line
  • East-West displacement = sum of East distances - sum of West distances
  • North-South displacement = sum of North distances - sum of South distances
  • Pythagorean triplets: (3,4,5), (5,12,13), (8,15,17), (7,24,25)
  • If movements form a rectangle, the diagonal is the shortest distance
  • The shortest distance is always ≤ total path length

Shortcut Methods to Solve Faster

Distance = √(EW² + NS²)
For perpendicular movements, use the Pythagorean theorem directly
For movements in the same line, distance = absolute difference
Recognize Pythagorean triplets for quick calculation

Common Mistakes to Avoid

Adding distances directly instead of using Pythagoras (path length vs displacement)
Forgetting to consider direction signs when calculating net displacement
Not squaring the net displacements before adding
Forgetting to take square root of the sum
Using Pythagoras when movements are collinear (should use subtraction)

Exam Importance

Shortest 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 Shortest 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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