Q5. Namita walks 14 meters towards the west, then turns right and walks 14…
2024
Q5. Namita walks 14 meters towards the west, then turns right and walks 14 meters, then turns left and walks 10 meters. She turns left again and walks 14 meters. What is the shortest distance (in meters) between her starting point and her current position?
- A.
10
- B.
24
- C.
32
- D.
45
Show answer & explanation
Correct answer: B
Concept
In a direction-sense problem, plot the walk on a coordinate plane: each right turn rotates the facing direction 90° clockwise and each left turn rotates it 90° counter-clockwise. The final answer is the straight-line (Euclidean) distance between the starting coordinate and the final coordinate — not the sum of the individual legs walked.
Application
Place the start S at the origin (0, 0), initially facing west.
Walk 14 m west: position becomes (−14, 0).
Turn right (facing west, a right turn points north) and walk 14 m: position becomes (−14, 14).
Turn left (facing north, a left turn points west) and walk 10 m: position becomes (−24, 14).
Turn left again (facing west, a left turn points south) and walk 14 m: position becomes (−24, 0).
Cross-check
The second leg (north, 14 m) and the fourth leg (south, 14 m) are equal in length and opposite in direction, so they cancel exactly — the y-coordinate returns to 0. The only net motion is horizontal: 14 m + 10 m = 24 m west of the start. Applying the distance formula independently, √((−24−0)² + (0−0)²) = 24 m, which confirms the same result.