Direction sense with two right turns: Gopal walks 2 km straight from his school, then turns right and walks 1 km, turns right again and walks 1 km to reach home. If his home lies south-east of the school, in which direction did he begin walking from the school?

Introduction / Context:The problem fixes the final relative bearing of home (south-east of school) and describes a 3-segment path with two consecutive right turns. We must infer the initial heading.

Given Data / Assumptions:

• Segment 1: 2 km, unknown initial direction.
• Segment 2: 1 km after a right turn.
• Segment 3: 1 km after another right turn.
• Home is south-east of school (positive x, negative y relative to school).

Concept / Approach:Two right turns advance the heading by 180° from the initial direction, and the two 1 km legs form perpendicular components. Test candidate initial headings and check the net displacement against “south-east.”

Step-by-Step Solution:

Verification / Alternative check:Only the “initial East” assumption yields a final vector with x > 0 and y < 0 (SE), matching the given relationship.

Why Other Options Are Wrong:

• North/West/South beginnings land in different quadrants or axes.

Common Pitfalls:Forgetting that the second and third segments are both 1 km; asymmetry would change the quadrant test.

Final Answer:East