Mapping the Movements: Boy's Path
Let's break down the boy's movement step-by-step, starting from point P.
- Initial Move: The boy walks 3 km straight towards the East.
- First Turn: He turns left (now facing North) and walks another 3 km. At this point, he is 3 km East and 3 km North of P.
- Second Turn: He turns left again (now facing West) and walks 3 km. This westward movement cancels out his initial eastward movement.
His final position is therefore 3 km North of the starting point P, on the line directly North of P.
Mapping the Movements: Girl's Path
Now, let's follow the girl's journey from the same starting point P.
- Initial Move: The girl walks 2 km straight towards the South.
- First Turn: She turns left (now facing East) and walks 3 km. At this point, she is 3 km East and 2 km South of P.
- Second Turn: She turns left again (now facing North) and walks 2 km. This northward movement cancels out her initial southward movement.
Her final position is therefore 3 km East of the starting point P, on the line directly East of P.
Determining the Boy's Direction Relative to the Girl
We need to find the direction of the boy's final location with respect to the girl's final location.
- Boy's Final Position: Directly 3 km North of P.
- Girl's Final Position: Directly 3 km East of P.
Let's consider the girl's final position as the reference point.
- To get from the girl's position (3 km East of P) to the boy's position (3 km North of P), one needs to move West by 3 km and North by 3 km.
- A movement involving both West and North directions corresponds to the North-West direction.
Therefore, the boy is in the North-West direction of the girl.
Important Questions from Direction and Distance
- Johny starts from Point A and drives 6 km towards the North. He then takes a right turn, drives 17 km, turns right and drives 13 km. He then takes a right turn and drives 8 km. He takes a final right turn, drives 7 km and stops at Point P. How far (shortest distance) and towards which direction should he drive to reach Point A again? (All turns are 90 degrees turns only unless specified.)
- Town Q is to the east of Town P. Town R is to the south of Town Q. Town S is to the east of Town R. Town T is to the south of Town S. Town U is to the east of Town T. What is the position of Town U with respect to Town Q?
- Binoy starts from Point Y and drives 16 km towards the north. He then takes a right turn and drives 43 km, then turns right and drives 38 km. He then takes a right turn and drives 19 km. He takes a final right turn, drives 22 km and stops at Point Z. How far (shortest distance) and in which direction should he drive in order to reach Point Y again? (All turns are 90-degree turns only unless specified.)
- Himank starts from Point A and drives 13 km towards West. He then takes a left turn, drives 3 km, turns left and drives 16 km. He then takes a left turn and drives 6 km. He takes a final left turn, drives 3 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are 90° turns only unless specified.)
- Shyam starts from Point A and drives 12 km towards east. He then takes a right turn,
drives 7 km, turns right and drives 5 km. He then takes a left turn and drives 9 km. He
takes a final right turn, drives 7 km and stops at Point P. How far (shortest distance) and
towards which direction should he drive in order to reach Point A again? (All turns are
$90^{\circ}$ turns only unless specified.)
