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Difficulty: EasyDirection and Distance Test

Match each movement sequence described in List-I with its corresponding final position relative to the starting point in List-II.

  • A person walks 3 km3\text{ km} North, then turns to his right and walks 4 km4\text{ km}.5 km5\text{ km} North-East
  • A person walks 4 km4\text{ km} East, then turns to his right and walks 3 km3\text{ km}.5 km5\text{ km} South-East
  • A person walks 3 km3\text{ km} South, then turns to his right and walks 4 km4\text{ km}.5 km5\text{ km} South-West
  • A person walks 4 km4\text{ km} West, then turns to his right and walks 3 km3\text{ km}.5 km5\text{ km} North-West

Answer

Sequence 1 matches 5 km5\text{ km} North-East, Sequence 2 matches 5 km5\text{ km} South-East, Sequence 3 matches 5 km5\text{ km} South-West, and Sequence 4 matches 5 km5\text{ km} North-West.
Each movement sequence consists of two perpendicular steps of lengths 3 km3\text{ km} and 4 km4\text{ km}. By the Pythagorean theorem, the net displacement magnitude is 5 km5\text{ km} in all cases. The directional quadrant depends on the facing direction prior to the right turn: North+Right points North-East, East+Right points South-East, South+Right points South-West, and West+Right points North-West.

Step-by-Step Solution

1
Determine orientation and turns for each movement path.
Facing North and turning right leads East. Facing East and turning right leads South. Facing South and turning right leads West. Facing West and turning right leads North.
A 90∘90^\circ clockwise rotation corresponds to a right turn.
2
Calculate the magnitude of shortest distance for each path using the Pythagorean theorem.
In all four cases, the perpendicular components are 3 km3\text{ km} and 4 km4\text{ km}. The shortest distance is 32+42=9+16=5 km\sqrt{3^2 + 4^2} = \sqrt{9 + 16} = 5\text{ km}.
The straight-line displacement forms a right-angled triangle.
3
Determine the resultant direction quadrant for each sequence.
(North, East) →\rightarrow North-East; (East, South) →\rightarrow South-East; (South, West) →\rightarrow South-West; (West, North) →\rightarrow North-West.
Combining two orthogonal direction vectors places the final point in the respective sub-cardinal quadrant.

Key Concept

Direction sense analysis, orthogonal turns, and Pythagorean distance calculation
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Topics

Direction and Distance Test

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