Roy: 2 km East, then 3 km North-West, then 5 km South, then 2 km West, then 6 km North. In which direction is he from the starting point?

Introduction / Context:
With one diagonal leg (NW) and several axial legs, we compute the final coordinates and then infer the quadrant relative to the start.

Given Data / Assumptions:

• Take East = +x, North = +y.
• NW of 3 km contributes (−3/√2, +3/√2) to (x, y).

Concept / Approach:
Sum all component vectors to get the final point and inspect signs of x and y to determine the direction.

Step-by-Step Solution:
Start (0,0) → after 2E: (2,0).+ 3NW ≈ (−2.121, +2.121) → (−0.121, 2.121).− 5S → (−0.121, −2.879).− 2W → (−2.121, −2.879).+ 6N → (−2.121, 3.121).x < 0 and y > 0 ⇒ North–West.

Verification / Alternative check:
A scaled sketch confirms the point lies up and left of the origin.

Why Other Options Are Wrong:
South-East/South-West/North-East do not match the (−x, +y) signs.

Common Pitfalls:
Dropping the diagonal components or treating NW as purely North or West.

Final Answer:
North – West