A boy and a girl are facing each other. If the boy is standing to the north west of the girl, then in which direction is the girl located with respect to the boy?

Introduction / Context:
This question is a simple relative direction problem. Instead of moving along a path, we compare the positions of two people directly. The phrase that one person is at the north west of another immediately implies the reverse relation by symmetry. Such questions are usually straightforward and are meant to check whether the candidate can mentally reverse directions without confusion.

Given Data / Assumptions:

• A boy and a girl are standing in such a way that they are facing each other.
• The boy is at the north west of the girl.
• We are asked for the direction of the girl with respect to the boy, not with respect to any external reference point.
• North west and south east are diagonal directions midway between the main cardinal directions.

Concept / Approach:
When we say that point B is at the north west of point G, it means that if we stand at G and move north and west simultaneously, we will reach B. In coordinate terms, B has a greater north component and a more westward component compared with G. The reverse relation from B to G is obtained by taking the opposite direction along both axes. The opposite of north is south and the opposite of west is east. Hence, from the boy's point of view, the girl must be to the south east.

Step-by-Step Solution:
Step 1: Imagine the girl at some point G on the ground.Step 2: The boy is at point B, which is to the north west of G. That means B lies up and to the left of G in a standard north up, east right diagram.Step 3: Now consider the direction from B back to G. To reach G from B, we must go downwards (south) and to the right (east).Step 4: Combining these two opposite directions gives the diagonal direction south east.Step 5: Therefore, with respect to the boy, the girl is located in the south east direction.

Verification / Alternative check:
This can be verified by thinking of a compass rose. North west and south east are opposite each other on the compass, forming a straight line through the centre. If one person is at north west relative to the other, the second person must be exactly at south east relative to the first. This symmetry property holds for other opposite pairs as well, such as north and south or north east and south west.

Why Other Options Are Wrong:
Option A (North) would be correct if the girl were directly south of the boy or if the given statement were reversed. Option B (South) ignores the east west component. Option C (East) takes only one component of the required direction. Only option D, south east, correctly combines south (opposite of north) and east (opposite of west) as required for the reverse relation.

Common Pitfalls:
Students sometimes mistakenly assume that if one person is north west of another, then the other is south west or north east, mixing up which axis to invert. The safe rule is that to reverse the relation, each component of the direction must be replaced by its exact opposite: north with south, east with west. When both components are changed, north west automatically becomes south east and vice versa.

Final Answer:
With respect to the boy, the girl is located in the south east direction, so the correct option is “South-East”.