West : North-East :: South : ? — Apply the same rotational shift on the compass to determine the corresponding direction for “South.”

Introduction / Context:
Direction analogies typically encode a fixed angular rotation on the compass rose. We must infer the exact rotation that maps “West” to “North-East” and then apply it to “South.”

Given Data / Assumptions:

• Compass bearings (in degrees from North): N 0°, E 90°, S 180°, W 270°.
• North-East (NE) is 45°.
• Rotation can be measured clockwise or counterclockwise; we only need consistency.

Concept / Approach:
Map West (270°) to North-East (45°). A counterclockwise rotation of 225° or, equivalently, a clockwise rotation of 135° accomplishes this (since 270° − 225° = 45°, and 270° + 135° ≡ 45° mod 360). Apply the same net rotation to South (180°). Using the simpler “+135° clockwise”: 180° + 135° = 315°, which corresponds to North-West (NW).

Step-by-Step Solution:
1) Determine rotation: W (270°) → NE (45°) = +135° clockwise.2) Apply to S (180°): 180° + 135° = 315°.3) 315° is North-West.

Verification / Alternative check:
Using the counterclockwise measure: 270° − 225° = 45°, likewise 180° − 225° = −45° ≡ 315° = NW. Both conventions confirm NW.

Why Other Options Are Wrong:

• South-East/East/North/South-West: Do not result from the same rotation applied to South.

Common Pitfalls:
Adding 90° or 180° mistakenly. Keep the rotation equal to that inferred from the first pair.

Final Answer:
North-west