Direction Sense

Snapshot

• Direction Sense describes a person walking and turning, then asks the final direction they face or their distance/direction from the start. Drawing the path on a compass turns it into simple geometry.
• The two ideas you need: the compass (N at top, E right, S down, W left, with the four diagonals) and the rule that a right turn is clockwise, a left turn anticlockwise — relative to the direction you are currently facing.
• This guide covers the compass, turning, shortest-distance (Pythagoras), shadows, and the "turn relative to facing" trap — with worked examples.
• Exam reality: +5 / −1. Sketch the path; don't track it in your head.

Part 1 — The compass and a worked path

Always orient your page with North up. Mark the start, then draw each leg with an arrow and its length. A left/right turn is taken from the direction you are facing now, not from North — this is the single biggest trap.

Part 2 — Shortest distance (the Pythagoras step)

If a person walks some distance North/South and some East/West, the straight-line distance from the start is the hypotenuse: distance = √(horizontal² + vertical²). In the path above (10 N, 10 E, 5 S) the net movement is 10 E and 5 N, so the distance from start = √(10² + 5²) = √125 ≈ 11.2, in the North-East direction. Watch for the Pythagorean triples (3-4-5, 6-8-10) the examiner loves.

Part 3 — Turning, shadows & special cases

• Turn relative to facing: facing South and turning left sends you East (not West) — rotate from the current heading.
• Clockwise / anticlockwise: a right turn is clockwise; two right turns reverse your direction; four bring you back.
• Shadows: at sunrise the sun is in the East, so shadows fall West; at sunset the sun is West and shadows fall East. At noon shadows are negligible. This is a recurring direction-sense question.

Part 4 — Speed techniques

1. Always sketch with North up and arrows for each leg.
2. Sum the N/S legs and the E/W legs separately — net vertical and net horizontal give both the distance (Pythagoras) and the final direction.
3. For "facing" questions, rotate from the current heading, not from North.
4. Memorise the triples to skip the square root.
5. For shadows, fix sunrise = East light ⇒ West shadow.

Part 5 — Worked examples

1. A man walks 4 km North, then 3 km East. Distance from start? √(4²+3²) = 5 km (North-East).

2. Facing East, he turns right. Now facing? Right of East is South.

3. Walks 5 N, 5 E, 5 S. Net: 5 E, 0 N/S ⇒ he is 5 km East of start.

4. Facing North, turns left, walks 3, turns left, walks 3. He faces South and is at 3 W, 3 S ⇒ South-West of start, √18 ≈ 4.24 km away.

5. At sunrise a pole's shadow falls towards a boy. Which way does he face? Sunrise shadow points West, so he faces West.

6. Walks 10 E, 10 N, 10 E. Net 20 E, 10 N ⇒ √(400+100) = √500 ≈ 22.4 km, North-East.

7. Two right turns from facing West ⇒ now facing East (reversed).

8. Facing South, turns left (⇒ East), walks 6, turns right (⇒ South), walks 8. Distance from start = √(6²+8²) = 10.

Part 6 — Common traps

• Turning from North instead of the current heading — the #1 error.
• Forgetting Pythagoras for the shortest distance.
• Shadow direction — sunrise light East ⇒ shadow West, and vice-versa.
• Direction vs distance — read which the question wants.
• Net vs total distance — "distance from start" is the straight line, not the path length walked.

Part 7 — How to use this page

Sketch the compass once, re-solve the eight examples on paper with North up, then attempt the practice set and the timed test.

One-line revision: draw with North up, turn relative to your current facing, add N/S and E/W legs separately, use √(h²+v²) for distance, and remember sunrise light is East so shadows fall West.