Space visualisation and orientation
Track your facing direction separately from your position, then calculate the final displacement.
Direction and displacement
- Use a compass cross: north is up, east right, south down, and west left. A right turn is clockwise; a left turn is anticlockwise.
- Track facing direction separately from position. A turn changes facing but does not move the person; a walk changes position.
- For a shortest straight-line distance, combine perpendicular net movements with the Pythagorean theorem: d = √(x² + y²).
- For a path that turns or retraces steps, first cancel opposite movements on each axis; do not confuse total distance travelled with final displacement.
Worked example
A person starts facing north, turns right, then left, then right again. Which direction are they facing?
Solution: North → east → north → east. The person faces east. Turns alone do not change the person's position.
Distance example
A person walks 6 m north and then 8 m east. The route is 14 m, but the shortest distance from the start is √(6² + 8²) = 10 m, toward the north-east.
Practice · original questions
- Facing south, you turn left. Which direction do you face?
- You walk 5 m west, then 12 m north. What is your shortest distance from the starting point?
- You face east, turn 180°, then turn right. Which direction do you face?
Show answers and reasoning
- East. A left turn from south points east.
- 13 m. The perpendicular net movements give √(5² + 12²) = 13 m.
- North. East → west after the half-turn; a right turn from west points north.