🧭 Direction Sense - Formula Sheet

🎯 Basic Directions

Main Directions

N (North) ↑ E (East) → S (South) ↓ W (West) ←

Sub-directions

NE (North-East) ↗ NW (North-West) ↖ SE (South-East) ↘ SW (South-West) ↙

Angle Relationships

Each main direction = 90° apart Each sub-direction = 45° from main directions

📊 Rotation Rules

Right Turn (90° clockwise)

North → East → South → West → North

Left Turn (90° anticlockwise)

North → West → South → East → North

Multiple Rotations

Right × 2 = 180° turn (opposite direction) Right × 3 = 270° turn = Left × 1 Right × 4 = 360° turn = original direction

🔢 Distance Calculations

Pythagoras Theorem

Distance² = (North-South distance)² + (East-West distance)² Distance = √[(NS)² + (EW)²]

Shadow Problems

Morning: Sun in East → Shadow to West Evening: Sun in West → Shadow to East Noon: Sun overhead → No shadow

⚡ Solving Approach

Step-by-Step Method

1. Draw starting point
2. Mark each movement with direction and distance
3. Track final position
4. Calculate required distance/direction

Coordinate Method

Let starting point = (0,0) North: +y, South: -y East: +x, West: -x Final position = (x₁ + x₂ + …, y₁ + y₂ + …)

📝 Quick Tips

1. Always draw a diagram
2. Use coordinate system for accuracy
3. Remember: Right = clockwise, Left = anticlockwise
4. Final position = Sum of all movements
5. Use Pythagoras for straight-line distance

Master Direction Sense - Draw diagrams, use Pythagoras! 🧭