Direction sense
Replace mental rotation with a small map and consistent north-east-south-west directions.
Draw a fixed compass#
Place north at the top, east right, south bottom, and west left. Mark the starting facing direction before applying turns.
A right turn from north faces east; a right turn from east faces south. The turn is relative to the current direction, not the page.
Use coordinates#
Represent east as positive horizontal movement and north as positive vertical movement. A move 4 east and 3 north ends at (4, 3), regardless of the route used.
The shortest distance back to the start is the straight-line displacement. For perpendicular movements of 3 and 4 units, it is 5 units.
Trace carefully#
Record every turn and segment. If the question asks which direction the person faces, the final turn matters even without movement. If it asks position from the start, use displacement.
Common mistakes#
Do not confuse the observer's left with the traveller's left. Do not add all distances when the question asks shortest distance.
Final check#
Redraw the route at a small scale, verify the final coordinate, and separately state final facing direction. Keeping these two outputs distinct prevents many errors.
Key points
- Fix north at the top before tracing movement.
- A right or left turn depends on the current facing direction.
- Coordinates help combine horizontal and vertical displacement.
- Distance travelled and straight-line displacement are different.