From the post office, Aditi walks 10 m towards the West. She turns left and walks 6 m, turns left again and walks 28 m, and then turns right and walks 18 m. How far and in which direction is she from the post office?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 30 m South-East
A left turn moves the facing direction one step anticlockwise (West → South → East) and a right turn moves the facing direction one step clockwise (East → South). Keep a running total of the distance from the post office; then use Pythagoras.
Facing West, 10 m: 10 m west of the post office
Turns left, now facing South, 6 m: 10 m west, 6 m south
Turns left, now facing East, 28 m: \(28-10=18\) m east, 6 m south
Turns right, now facing South, 18 m: 18 m east, \(6+18=24\) m south
Distance \(=\sqrt{18^{2}+24^{2}}=\sqrt{324+576}=\sqrt{900}=30\) m
She is south and east of the post office, so the direction is South-East
Aditi is 30 m South-East of the post office.
