A girl walks 12 kms south from her house, turns left and walks 26 kms, again…
2023
A girl walks 12 kms south from her house, turns left and walks 26 kms, again turns left and walks 37 kms. Again she turns right and walks 6 kms to reach her office. In which direction is the office of the girl from her house?
Answer: C. North-East — CONCEPTA route can be represented as a coordinate displacement: east-west movements form the horizontal component, while north-south movements form the…
- A.
South-East
- B.
South
- C.
North-East
- D.
South-West
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Show answer & explanation
Correct answer: C
CONCEPT
A route can be represented as a coordinate displacement: east-west movements form the horizontal component, while north-south movements form the vertical component. A left or right turn is interpreted relative to the traveller’s current facing direction. The signs of the final horizontal and vertical components determine the quadrant direction.
APPLICATION
Place the house at (0, 0), taking east as positive x and north as positive y.
Walking 12 km south changes the position to (0, -12).
While facing south, a left turn points east; walking 26 km changes the position to (26, -12).
While facing east, a left turn points north; walking 37 km changes the position to (26, 25).
While facing north, a right turn points east; walking 6 km changes the position to (32, 25). Both components are positive, so the office lies to the North-East of the house.
CROSS-CHECK
Horizontal component: 26 + 6 = 32 km east.
Vertical component: 37 - 12 = 25 km north.
The two independent component totals place the office in the North-East quadrant.
Result: North-East.