Types
- Walks: a person walks, turns left/right and walks again; find final direction or distance from the start (generated on this site).
- Point networks: "Point A is 8 m west of B, C is 6 m north of B..." find direction or shortest distance between two points.
- Coded directions: 'P # Q means P is 3 m north of Q' and an expression such as A # B $ C @ D.
- Shadow questions: sunrise / sunset and the side on which a shadow falls.
The coordinate method (fastest and error-free)
- Put the reference point at (0, 0). East = +x, West = -x, North = +y, South = -y.
- Translate every clue into a coordinate: "C is 6 m north of B" gives C = (0, 6).
- Direction of X with respect to Y: look at (X - Y). Positive x and positive y is north-east, positive x and negative y is south-east, and so on. If one difference is zero the direction is a pure N, S, E or W.
- Shortest distance = square root of (dx squared + dy squared). Learn the triples 3-4-5, 5-12-13, 6-8-10, 8-15-17, 7-24-25.
Turning rules for walks
| Facing | After a right turn | After a left turn |
|---|---|---|
| North | East | West |
| East | South | North |
| South | West | East |
| West | North | South |
Shadow rule
Morning: the sun is in the east, so shadows fall towards the west. Evening: the sun is in the west and shadows fall towards the east. If in the morning the shadow falls to your right, your right is west, so you are facing south. (No shadow at noon is the usual exam assumption, so noon questions are rare.)
Worked example
A is 8 m west of B; C is 6 m north of B; D is 4 m east of C; E is 11 m south of D. With B = (0, 0): A = (-8, 0), C = (0, 6), D = (4, 6), E = (4, -5). E - A = (12, -5): east and south, so E is south-east of A, and AE = square root of (144 + 25) = 13 m.
Trap: "the direction of A with respect to B" means stand at B and look at A. Reversing the two gives the opposite direction (north-east becomes south-west).
Time target
40-60 seconds per question. Coded-direction sets: decode once and reuse the coordinates.