Minimum Distance

Minimum Distance problems ask for the shortest possible distance between two points, typically after a person walks in perpendicular directions. The minimum distance is always the straight line connecting the start and end points, calculated using the Pythagorean theorem.

10Worksheets
200+Practice Questions
IntermediateDifficulty
1-2 hoursHours to Master

Introduction to Minimum Distance

Minimum Distance problems ask for the shortest possible distance between two points, typically after a person walks in perpendicular directions. The minimum distance is always the straight line connecting the start and end points, calculated using the Pythagorean theorem.

Prerequisites

Pythagorean theorem Net displacement concept Right angle geometry Square root calculation
Why This Matters: Minimum Distance problems appear in 1-2 questions in SSC CGL and Banking PO exams. They test understanding of displacement vs path length.

How to Solve Minimum Distance Problems

1

Step 1: Track net East-West and North-South displacements

2

Step 2: These net displacements form perpendicular legs

3

Step 3: Minimum distance = √(EW² + NS²)

4

Step 4: Calculate the square root

5

Step 5: Answer with the distance

6

Step 6: Direction can also be specified if asked

Pro Strategy: The minimum distance is always the straight line displacement. Ignore the actual path taken; only net displacement matters.

Example Problem

Example: A person walks 5 m West, then 12 m South. What is the minimum distance from start? Solution: Step 1: Net West = 5 m, Net South = 12 m Step 2: These are perpendicular (West and South) Step 3: Minimum distance = √(5² + 12²) = √(25 + 144) = √169 = 13 m Answer: 13 m

Pro Tips & Tricks

  • Minimum distance = √(EW² + NS²)
  • Recognize Pythagorean triplets for quick answers
  • If movements are collinear, minimum distance = |net displacement|
  • The actual path length is always ≥ minimum distance

Shortcut Methods to Solve Faster

For perpendicular movements (3,4): min distance = 5
For perpendicular movements (5,12): min distance = 13
For perpendicular movements (8,15): min distance = 17

Common Mistakes to Avoid

Adding path distances instead of using net displacement
Not recognizing perpendicular directions
Forgetting to take square root

Exam Importance

Minimum Distance 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
1-2 questions
CAT
0-1 questions
INSURANCE
1-2 questions

Ready to Master Minimum 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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