Point A is to the south-east of point B. In which direction is point B with respect to point A?

Introduction / Context:
This is a simple conceptual question about opposite directions on the compass. We are told the relative position of point A with respect to point B and asked to reverse the perspective and describe where B lies with respect to A. Such questions test understanding of how opposite diagonal directions relate to each other on a compass.

Given Data / Assumptions:
- Point A is located to the south east of point B. - South east means A is both south and east of B. - We must state where B is relative to A. - Directions are standard: north, south, east, west, and the four diagonals.

Concept / Approach:
If A is south east of B, then from B you move downwards (south) and to the right (east) to reach A. To reverse the viewpoint, we imagine standing at A and asking in which diagonal we must look to see B. The reverse of south is north and the reverse of east is west. Therefore, the opposite diagonal to south east is north west. This reasoning relies on the symmetry of the compass and the idea that relative positions are reversible by switching to opposite directions.

Step-by-Step Solution:
1. Take B as the reference. A is described as lying to the south east of B. 2. South east combines the south and east directions; so A is below and to the right of B on a standard map. 3. Now take A as the reference point and imagine where B must be relative to A. 4. To move from A to B, we must undo the previous movement. Instead of going south and east, we go north and west. 5. North plus west together give the diagonal direction north west. 6. Therefore, B is to the north west of A.

Verification / Alternative check:
Draw a simple coordinate system. Place B at the origin (0, 0). Represent A at some coordinates (1, -1) where the positive x axis is east and the positive y axis is north. From B, A is at south east. From A, B is at (-1, 1), which clearly points to the north west. This small diagram confirms the mental reasoning about opposite diagonals without relying on algebraic formulas.

Why Other Options Are Wrong:
- South West would place B below and to the left of A, which does not match the given relation. - North East would correspond to A being south west of B, not south east. - South East repeats the original direction but in the wrong sense; it is the direction from B to A, not from A to B. - Directly South ignores the east west component and is incomplete for a diagonal relationship.

Common Pitfalls:
Students sometimes forget that reversing relative position means flipping both components of a diagonal direction, not just one. Another mistake is to think that if A is south east of B then B must also be south east of A, which is incorrect. Always consider that moving from A to B uses opposite directions compared to moving from B to A.

Final Answer:
Point B is to the north west of point A.