Radhika walks 50 m South from home, then 20 m East, then 30 m North, and then heads straight back home. In which direction is she walking at that last step?

Introduction / Context:
We track Radhika’s current location relative to home and then determine the bearing of the straight line from that location back to home.

Given Data / Assumptions:

• South 50 → (0, −50)
• East 20 → (20, −50)
• North 30 → (20, −20)
• Home is at (0, 0).

Concept / Approach:
The direction while walking home is the direction of the vector from current position (20, −20) to (0, 0), i.e., (−20, +20).

Step-by-Step Solution:
Current position: (20, −20).Vector to home: (0 − 20, 0 − (−20)) = (−20, +20).x < 0 → West component; y > 0 → North component.Hence, the direction is North-West.

Verification / Alternative check:
Sketch shows the point lies 20 m East and 20 m South of home; returning path goes diagonally up-left (North-West).

Why Other Options Are Wrong:
North alone lacks the West component; East/South-East point away from home.

Common Pitfalls:
Confusing “direction from home” with “direction towards home.” The question asks the latter.

Final Answer:
North - West