Introduction
Direction & Distance questions trace someone's movement across compass directions and ask for their final
direction/position from the starting point, or the shortest straight-line distance back to start.
Turn Logic
| Turn | Effect |
|---|
| Right turn (clockwise) | North→East→South→West→North |
| Left turn (anti-clockwise) | North→West→South→East→North |
| 180° turn | Faces the exact opposite direction |
Shortest Distance Formula
When movement forms a right angle (e.g., some distance North, then some distance East), the shortest distance
back to the starting point is the hypotenuse: Distance = √(a² + b²), using the Pythagoras theorem.
Q. Raj walks 8 km North, then turns right and walks 6 km. How far is he from his starting point?
North then right turn = now facing East, walked 6 km. This forms a right angle: 8 km and 6 km as the two legs.
Distance = √(8² + 6²) = √(64+36) = √100 = 10 km.
Q. A man walks 5 km East, then turns left and walks 5 km, then turns left again and walks 5 km. In which direction is he now from his starting point?
Start facing East, walk 5 km. Turn left → facing North, walk 5 km. Turn left again → facing West, walk 5 km.
Net movement: East 5 km cancels with West 5 km (equal and opposite) → net displacement is purely 5 km North.
Answer: he is North of the starting point.
⚠️ Key Insight: Track movement along two axes separately (East-West net, North-South net)
instead of visualising the whole path at once — this avoids losing track after 3+ turns.
💡 Exam Tip: The Pythagoras shortcut only applies when the net East-West and North-South
movements form a clean right angle — if movements partially cancel first, calculate the net leg lengths before
applying the formula.
✅ Practice Focus: Left/right turn sequencing · Net displacement along two axes · Shortest
distance using Pythagoras · Final-direction-facing questions after multiple turns.