A drives 10 km towards the East. He then turns to his right and drives 3 km.…
2025
A drives 10 km towards the East. He then turns to his right and drives 3 km. He then turns to his right again and drives 3 km towards the West. He then turns to his left and drives 2 km. Finally, he turns to his right and drives 7 km. How far is he from his starting point, and in which direction?
- 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, track the current facing direction after every turn: a right turn rotates the heading 90 degrees clockwise (East to South to West to North to East), and a left turn rotates it 90 degrees anticlockwise. Add up the East-West distances separately from the North-South distances, then read the final distance and direction straight off whichever axis is non-zero.
Start at the origin, facing East. Move 10 km East.
Turn right (East to South). Move 3 km South.
Turn right again (South to West). Move 3 km West.
Turn left (West to South). Move 2 km South.
Turn right (South to West). Move 7 km West.
Net East-West: 10 km East minus 3 km West minus 7 km West = 0 km -- the horizontal component cancels out completely.
Net North-South: 3 km South plus 2 km South = 5 km South -- both southward legs add up in the same direction.
Cross-check: plotting the same five legs on a compass grid, as in the figure below, traces a path that lands directly south of the starting point with no residual east-west offset.
So the final position is 5 km South of the starting point -- magnitude 5 km, direction South.