Naomi runs for 10 km in the eastern direction. She then turns left and starts…
2023
Naomi runs for 10 km in the eastern direction. She then turns left and starts walking for 6 km. Again, she turns left and starts running for 6 km. Then she turns left and walks again for 6 km. How far is she from the starting point?
- A.
4 KM
- B.
5 KM
- C.
7 KM
- D.
8 KM
Show answer & explanation
Correct answer: A
Concept: In direction-and-distance problems, track each turn using the left/right turn rule relative to the current facing direction, decompose the path into net East-West and net North-South components, and the straight-line distance from the start is the resultant of these two components (equal to the single non-zero component when the other axis cancels to zero, or found via the Pythagorean theorem when both axes have a net value).
Application: Naomi starts facing East and takes three consecutive left turns, so her successive facing directions are East, then North, then West, then South.
Runs 10 km East: position moves from (0, 0) to (10, 0).
Turns left (now facing North) and walks 6 km: position moves to (10, 6).
Turns left again (now facing West) and runs 6 km: position moves to (4, 6).
Turns left again (now facing South) and walks 6 km: position moves to (4, 0).
Cross-check: The North (6 km) and South (6 km) legs cancel exactly, so the net North-South displacement is 0. The net East-West displacement is 10 km (East) minus 6 km (West) equals 4 km (East). Since the North-South component is zero, the straight-line distance from the starting point equals the East-West component alone: 4 km.
Therefore, Naomi is 4 km from her starting point.