Cardinal Directions — Revision Notes

⚡ 30-Second Revision

Convention: east = +x; north = +y.
Turns update facing; movements update position.
Path length adds legs; displacement joins endpoints.
Relative position subtracts coordinates in one frame.
A quadrant is not an exact bearing.
These are original exercises under the 2026 Paper II reasoning syllabus.

2-Minute Revision

Separate three questions before calculating: where is the traveller, which way are they facing, and how far have they moved? Translate each leg into a signed coordinate change and maintain the current-facing arrow separately.

For two people, use a shared origin and subtract final coordinates in the requested order. Opposite reference directions have the same separation. Use the Pythagorean relation only for perpendicular components, and preserve units.

A route that returns to its start has zero displacement even though its path length is positive. If a distance or turn is missing, test whether more than one final position remains possible.

5-Minute Revision

Five-minute reconstruction

A courier begins at the origin facing east, walks 9 metres, turns left and walks 12 metres, then turns left and walks 4 metres. Write the positions (9, 0), (9, 12) and (5, 12). The courier faces west, stands northeast of the origin and is 13 metres from it by the shortest route. The travelled distance is 25 metres.

Now place another person at (5, 3). The courier is directly north of that person by 9 metres. This relative comparison uses the second person's position as reference; it does not change the courier's original route.

Explain why 25 metres, 17 metres and west can each be meaningful observations but fail a question asking for shortest distance from the start. They are respectively path length, the sum of net components and facing direction. The correct answer depends on the requested quantity.

Vyyuha Quick Recall

P-F-D: Position, Facing, Distance. Keep three records, then select the one the question asks for.