Direction questions test whether you can follow a path and read the final bearing or the straight-line distance back to the start. Always draw a small compass and plot each leg.
Direction rules
A right turn while facing North points you East; another right faces South (turns are clockwise). Sunrise is in the East, sunset in the West — morning shadows fall West, evening shadows East. For straight-line distance from start, the legs form a right triangle: distance = sqrt(a^2 + b^2).
- A right turn while facing North points you East; another right faces South (turns are clockwise).
- Sunrise is in the East, sunset in the West — morning shadows fall West, evening shadows East.
- For straight-line distance from start, the legs form a right triangle: distance = sqrt(a^2 + b^2).
How to Approach It
- Draw a compass with north up — Begin each problem with a fresh compass so that left and right are never ambiguous. Plot the starting point and then each leg of the journey in turn.
- Re-orient after every turn — A turn is always relative to your current facing, not to the page. Update the facing direction before you plot the next leg.
- Find the net displacement — The straight-line distance back to the start uses the perpendicular legs as a right triangle, so apply Pythagoras — and recognise the 3-4-5 and 5-12-13 triples on sight.
- Lean on turn-pairs and shadows — Two turns the same way reverse your facing, and morning shadows fall west while evening shadows fall east. These give instant answers to facing questions.
Techniques & Methods
- Compass on the page — Keep north up and redraw your facing after every turn.
- Turns in pairs reverse — Two right turns (or two left turns) flip your facing by 180°.
- Pythagoras for displacement — Perpendicular legs give a right triangle; know 3-4-5 and 5-12-13. e.g. 6 km N, 8 km E → 10 km from start.
- Shadow rule — Morning shadows fall west; evening shadows fall east.
The Edge
When the path goes North then East (or any two perpendicular legs), the displacement is the hypotenuse. Memorise the 3-4-5 and 5-12-13 triples — most questions are built on them. Two right turns reverse your facing; two left turns do the same. Count turns in pairs to fast-track the final direction.Worked example
A person walks 3 km north, then 4 km east. How far is she from the start?
- Sketch it: she goes 3 km north, then turns and goes 4 km east, and north and east meet at a right angle.
- The straight-line distance back to the start is the hypotenuse of a right triangle with legs 3 and 4.
- Apply Pythagoras: distance = sqrt(3² + 4²) = sqrt(9 + 16) = sqrt(25).
- sqrt(25) = 5, so she is 5 km from the start. (This is the familiar 3-4-5 triangle.)
Answer: 5 km from start
Worked example
Facing north, a man turns right, then right again. Which way does he now face?
- Start facing north and turn right (clockwise): he now faces east.
- Turn right again from east: he now faces south.
- A useful check: two right turns add up to 180°, which reverses the original facing.
- North reversed is south, confirming the result.
Answer: He faces South
Worked Drills
Worked example
A man walks 12 km north, then 5 km east. His straight-line distance from the start is: (a) 13 km b) 15 km c) 17 km d) 18 km)
- The two legs are perpendicular, forming a right triangle with legs 12 and 5.
- distance = sqrt(12² + 5²) = sqrt(144 + 25) = sqrt(169).
- sqrt(169) = 13 (the 5-12-13 triple).
Answer: 13 km — option a)
Worked example
From a point, a person goes 4 km west, then 3 km north, then 4 km east. He is now: (a) 3 km North of start b) 5 km NE c) 4 km East d) 7 km away)
- The 4 km west and 4 km east cancel exactly.
- Only the 3 km north remains.
- So he is 3 km north of the start.
Answer: 3 km North of start — option a)
Worked example
A starts and walks 6 km east; B starts from the same point and walks 8 km north. The distance between them is: (a) 8 km b) 10 km c) 12 km d) 14 km)
- Their paths are perpendicular (east vs north).
- Distance between = sqrt(6² + 8²) = sqrt(36 + 64) = sqrt(100).
- sqrt(100) = 10.
Answer: 10 km — option b)
Worked example
In the morning, a man walks directly towards his own shadow. He is moving towards the: (a) East b) West c) North d) South)
- In the morning the sun is in the east, so shadows fall toward the west.
- Walking toward his own shadow means walking west.
Answer: West — option b)
Worked example
A man walks 1 km north, 1 km east, 1 km north, 1 km east. His overall direction from the start is: (a) North-East b) North-West c) South-East d) South-West)
- Add the north legs: 1 + 1 = 2 km north.
- Add the east legs: 1 + 1 = 2 km east.
- Equal north and east displacement points north-east.
Answer: North-East — option a)
Worked example
Facing south, a man turns left, walks, then turns left again. He now faces: (a) North b) South c) East d) West)
- Facing south, a left turn points him east.
- A second left turn from east points him north.
Answer: North — option a)
Worked example
Walk 9 km west then 12 km south. Distance from start: (a) 13 km b) 15 km c) 17 km d) 21 km)
- West and south are perpendicular legs.
- distance = sqrt(9² + 12²) = sqrt(81 + 144) = sqrt(225).
- sqrt(225) = 15.
Answer: 15 km — option b)
⚠ Watch out
- "Right" and "left" are relative to the current facing, not the page.
- Net displacement is the straight line, not the total distance walked.
- Re-orient your compass after every turn before plotting the next leg.
Takeaways
- Draw a fresh compass with north up for every problem.
- Update your facing after each turn before plotting the next leg.
- Straight-line distance is Pythagoras — memorise 3-4-5 and 5-12-13.
- Two same-direction turns reverse your facing; opposite legs cancel.