41  Directions

41.1 Introduction

Direction sense problems test spatial reasoning and the ability to follow movements or turns in the four cardinal directions: North, South, East, West. Sometimes diagonals (NE, NW, SE, SW) or angular rotations are also used. These questions require careful step-by-step tracking.

41.2 1) Core Concepts

41.2.1 1.1 Cardinal Directions

  • Four main: North, South, East, West.
  • Four intermediate: North-East (NE), North-West (NW), South-East (SE), South-West (SW).
  • In diagrams:
    • North ↑
    • South ↓
    • East →
    • West ←

41.2.2 1.2 Turns

  • Left turn: 90° anticlockwise.
  • Right turn: 90° clockwise.
  • About turn / U-turn: 180°.

41.2.3 1.3 Distance

Use Pythagoras theorem when diagonal movement is implied.
If someone goes 3 km North and 4 km East, displacement = \(\sqrt{3^2+4^2} = 5\) km NE.

41.3 2) Types of Problems

  1. Simple direction finding → After movement and turns, final facing direction.
  2. Distance and displacement → Compute shortest distance from start point.
  3. Coded directions → Symbols represent moves.
  4. Relative position → One person’s position relative to another’s.

41.4 3) Solving Strategy

  1. Draw diagram step by step.
  2. Mark turns clearly (left/right).
  3. Use coordinates method: start at (0,0), add/subtract values.
    • North (+y), South (−y), East (+x), West (−x).
  4. For diagonals, break into x and y components.

41.5 4) Solved Examples

41.5.1 Example 1

A man walks 3 km North, then 4 km East. How far is he from the starting point?
- Displacement = \(\sqrt{3^2+4^2} = 5\) km.
Answer: 5 km NE.

41.5.2 Example 2

A person faces North, turns right, walks 4 m, turns left, walks 3 m. Which direction is he facing?
- Facing North → right turn = East.
- Moves East, then turns left → faces North again.
Answer: North.

41.5.3 Example 3

A boy walks 2 km South, then 2 km East, then 2 km North. How far is he from start?
- Path: (0,0) → (0,−2) → (2,−2) → (2,0).
- Displacement = \(\sqrt{2^2+0^2} = 2\) km East.
Answer: 2 km East.

41.5.4 Example 4

Ravi walks 5 km West, turns right, and walks 5 km. What is his final position relative to start?
- Start (0,0).
- 5 km West → (−5,0).
- Right turn from West → North.
- 5 km North → (−5,5).
Answer: 5 km North-West.

41.5.5 Example 5

A person walks 10 km North, then 10 km East, then 10 km South. How far from starting point?
- Path: (0,0) → (0,10) → (10,10) → (10,0).
- Displacement = \(\sqrt{10^2+0^2} = 10\) km East.
Answer: 10 km East.

41.6 5) Practice Questions

  1. A person walks 4 km North, then 3 km East, then 4 km South. How far and in which direction is he from the start?
  2. Starting from facing East, a person makes 3 consecutive right turns and walks 2 km each time. Which direction is he facing?
  3. A man walks 6 km West, then 8 km North. How far is he from the start?
  4. A person walks 5 km South, then 5 km East, then 5 km North. How far and in which direction is he from the start?
  5. If A is standing North of B, and C is East of A, then in which direction is C with respect to B?

41.7 6) Answer Key

  1. Path: (0,0) → (0,4) → (3,4) → (3,0). Final (3,0). Distance = 3 km East.
  2. Facing East → right = South → right = West → right = North. North.
  3. Displacement = \(\sqrt{6^2+8^2} = 10\) km North-West.
  4. Path: (0,0) → (0,−5) → (5,−5) → (5,0). Distance = 5 km East.
  5. If A is North of B, and C is East of A, then C is North-East of B.

41.8 Summary

  • Always mark movements step by step.
  • Use coordinate geometry method to avoid confusion.
  • Distinguish between distance traveled and displacement.
  • Turning directions (left/right) must be tracked carefully.
  • Pythagoras theorem is essential for displacement problems.