From her house, Pallavi walks 6 m towards the East. She turns left and walks 10 m, turns left again and walks 13 m, and then turns right and walks 14 m. How far and in which direction is she from her house?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 25 m North-West
A left turn moves the facing direction one step anticlockwise (East → North → West) and a right turn one step clockwise (West → North). Keep a running total of the distance from the house; then use Pythagoras.
Facing East, 6 m: 6 m east of the house
Turns left, now facing North, 10 m: 6 m east, 10 m north
Turns left, now facing West, 13 m: \(13-6=7\) m west, 10 m north
Turns right, now facing North, 14 m: 7 m west, \(10+14=24\) m north
Distance \(=\sqrt{7^{2}+24^{2}}=\sqrt{49+576}=\sqrt{625}=25\) m
She is north and west of the house, so the direction is North-West
Pallavi is 25 m North-West of her house.
