The compass and turns
The four main directions are north (N), east (E), south (S) and west (W), with the intermediate ones north-east (NE), south-east (SE), south-west (SW) and north-west (NW). Facing north, a right turn leads to east and a left turn to west. Facing east, a right turn leads to south. Each right turn is 90° clockwise and each left turn 90° anticlockwise.
A method
- Draw a compass at the top of your rough work and mark the start as (0, 0).
- Treat east and north as positive. A move of 5 m east is (+5, 0); 3 m south is (0, −3).
- Update the facing direction at each turn.
- Add the moves to get the final coordinates.
- Find the distance with Pythagoras if both coordinates are non-zero, and the direction from the signs.
Worked examples
Example 1. A man walks 6 km north, then 8 km east. His distance from the start is √(6² + 8²) = 10 km, to the north-east of the start.
Example 2. A person starts facing north, walks 10 m, turns right and walks 5 m, turns right again and walks 10 m. Moves: (0, +10), then east (+5, 0), then south (0, −10). Final = (5, 0): 5 m east of the start.
Example 3. Starting at a point, Ria goes 4 km west, 3 km south and 4 km east. Coordinates: (−4, 0), then (−4, −3), then (0, −3). She is 3 km south of the start.
Example 4 (turns). Facing east, a person turns left, then left again and then right. After the first left: north; the second left: west; right: north. She faces north.
Example 5 (shadows). In the morning, the sun is in the east, so a shadow falls to the west. If a person's shadow falls to their right in the morning, they are facing south (west is on their right when facing south). In the evening, shadows fall towards the east.
Example 6 (shortest path). A moves 12 m south, then 5 m west. His distance from the start is √(144 + 25) = 13 m, to the south-west.
Example 7 (two people). A walks 6 km east and B walks 8 km north from the same point. The distance between them is 10 km.
Common traps
- Confusing left and right with compass directions after several turns.
- Dropping the facing direction after a turn.
- Stating the final direction as the last move direction instead of the position relative to the start.
- Using Pythagoras when moves are in the same line.
Speed tips
- Memorise the right-angle triples 3-4-5, 5-12-13 and 8-15-17.
- Sketch every problem, even simple ones.
- Cancel opposite moves before computing distance.
A practice routine
- Day 1: single-turn problems and facing directions.
- Day 2: multi-step paths with coordinates.
- Day 3: shadow problems and two-person problems.
- Day 4: a timed set of 12 at 45 seconds each.
Where it appears
Direction sense appears in banking reasoning, SSC CGL reasoning, railway reasoning and CUET General Test papers. Related: blood relations and coding-decoding.
Practice tests below are published by institutes and educators on TestMint.
