Lakshmi starts from point ‘A’ and travels 2 km Southwards to a point ‘Z’ and…
2023
Lakshmi starts from point ‘A’ and travels 2 km Southwards to a point ‘Z’ and then turns right and travels twice that distance to reach ‘Y’. She then turns left and travels five times the distance she covered between point ‘A’ and ‘Z’ and reaches point ‘X’. From there she turns left and travels 4 km to reach destination ‘B’. What is the shortest distance between the points ‘A’ and ‘B’ and what is B’s direction with respect to ‘A’?
- A.
12 km, South
- B.
8 km, North
- C.
8 km, South
- D.
12 km, North
Attempted by 133 students.
Show answer & explanation
Correct answer: A
Step-by-step movement:
A → Z = 2 km (South)
Z → Y = 4 km (West) [right turn from South; twice 2 km]
Y → X = 10 km (South) [left turn from West; five times 2 km]
X → B = 4 km (East) [left turn from South]
Combine horizontal moves: 4 km West and 4 km East cancel, so net horizontal displacement = 0 km.
Combine vertical moves: 2 km South + 10 km South = 12 km South, so net vertical displacement = 12 km South.
Coordinates:
A = (0, 0)
B = (0, -12)
Shortest distance = sqrt((0)^2 + (-12)^2) = 12 km.
Answer: Shortest distance = 12 km; Direction of B with respect to A = South.