Grid of neighbors at 200 m diagonals: Rahim is at the origin. Babu: 200 m north-west; Joseph: 200 m south-west; Gopal: 200 m south-east of Joseph; Roy: 200 m north-east of Gopal. Where is Roy relative to Babu?

Difficulty: Medium

Correct Answer: South east

Explanation:


Introduction / Context:
This is a composition of diagonal moves (NW, SW, SE, NE) on a square grid with equal step lengths (200 m). We compare Roy’s final coordinates to Babu’s coordinates.


Given Data / Assumptions:

  • Use unit steps for direction; distance equality preserves direction labels.
  • Babu from Rahim: NW = (−1, +1).
  • Joseph from Rahim: SW = (−1, −1).
  • Gopal from Joseph: SE = (+1, −1).
  • Roy from Gopal: NE = (+1, +1).


Concept / Approach:
Compute coordinates relative to Rahim, then subtract to get Roy relative to Babu.


Step-by-Step Solution:

Babu = (−1, +1).Joseph = (−1, −1).Gopal = (−1, −1) + (+1, −1) = (0, −2).Roy = (0, −2) + (+1, +1) = (1, −1).Roy − Babu = (1 − (−1), −1 − 1) = (2, −2) ⇒ South-East.


Verification / Alternative check:
Diagramming a 2×2 diamond centered near Rahim shows Roy diagonally opposite Babu along the SE diagonal.


Why Other Options Are Wrong:

  • South-west/North/North-east do not match the computed relative vector.


Common Pitfalls:
Mixing “relative to Rahim” with “relative to Babu.” Always subtract the reference point’s coordinates.


Final Answer:
South east

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