Lesson 4 of 5 | Reasoning Methods
Direction and Distance with Coordinates
Reasoning Methods
Reliable representation
Use coordinates: east +x, west −x, north +y, south −y. Update position after every move; do not rely on a mental sketch.
Worked example
Start at (0,0), move 5 km north, 3 km east, then 1 km south. Final point is (3,4). Straight-line distance is √(3²+4²)=5 km, and the direction from the start is north-east.
Turn questions
Track facing separately from position. A right turn changes north→east→south→west. Draw a four-direction compass and rotate one quarter-turn per 90° instruction.
Checks
- Net east-west and north-south movements separately.
- Distinguish path length from displacement.
- Confirm whether the question asks current facing or direction from the start.