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.