A drives 10 km towards the east and then turns right, driving 3 km. He again…
2024
A drives 10 km towards the east and then turns right, driving 3 km. He again turns right and drives 3 km towards the west. He then turns left and drives 2 km. Finally, he turns right and travels 7 km. How far is he from his starting point, and in which direction is he located?
- A.
10 km, East
- B.
9 km, North
- C.
8 km, West
- D.
5 km, South
Show answer & explanation
Correct answer: D
Concept
In a direction-sense problem, treat every straight-line move as a vector on the compass plane (East = +x, North = +y). A right turn rotates the current heading 90° clockwise; a left turn rotates it 90° counter-clockwise. The final displacement from the start is the vector sum of every leg, and the distance from the start is only the straight-line (net) displacement - not the total distance walked.
Application
Start at A facing East; walk 10 km East to point B.
At B, turn right (East to South) and walk 3 km South to C.
At C, turn right again (South to West) and walk 3 km West to D.
At D, turn left (West to South) and walk 2 km South to E.
At E, turn right (South to West) and walk 7 km West to F.
Cross-check
Net east-west shift: +10 (East) - 3 (West) - 7 (West) = 0. Net north-south shift: 3 km South + 2 km South = 5 km South, with no northward leg to offset it. Since the east-west component is zero, the straight-line distance from the start equals the net south component.
Result
Therefore, F is exactly 5 km due south of the starting point A.