Understanding the Direction Transformation

This question involves a specific Direction Transformation applied to the standard compass directions. We are given that South-West becomes North, and we need to find what North-West will become under the same transformation. This is a common type of spatial reasoning problem involving compass directions.

Analyzing the Transformation Rule

The rule is: "If South-West becomes North". This means the position that was originally South-West is now designated as North. We need to understand the nature of this shift. A common approach to solving such logical reasoning problems is to determine the relative shift.

Let's consider the relative positions on a standard compass rose based on angles clockwise from North (0°):

• North: $0^\circ$ or $360^\circ$
• North-West: $315^\circ$
• West: $270^\circ$
• South-West: $225^\circ$
• South: $180^\circ$
• East: $90^\circ$

We are given that the direction that was originally South-West ($225^\circ$) is now called North (the new $0^\circ$ reference). We need to find what the direction that was originally North-West ($315^\circ$) is called under this new system.

Determining the Relative Shift

Let's find the relationship between the direction we need to transform (North-West) and the original reference direction (North). North-West is $315^\circ$ clockwise from North, or more simply, $360^\circ - 315^\circ = 45^\circ$ counter-clockwise from North.

The rule of the Direction Transformation seems to be: find the position of the target direction relative to the original North, and apply that same relative position starting from the direction that is now designated as North (which is the original South-West).

Applying the Rule to North-West

The relative position of North-West from the original North is $45^\circ$ counter-clockwise.

We apply this same relative shift ($45^\circ$ counter-clockwise) starting from the position that is now considered North, which is the original South-West ($225^\circ$).

Starting from the original position of South-West ($225^\circ$), move $45^\circ$ counter-clockwise:

$225^\circ - 45^\circ = 180^\circ$

The direction at $180^\circ$ on a standard compass rose is South.

Step-by-Step Solution

1. Identify the initial condition: South-West becomes North.
2. Identify the direction to transform: North-West.
3. Determine the relative position of North-West from the original North: North-West is $45^\circ$ counter-clockwise from North.
4. Apply this relative shift ($45^\circ$ counter-clockwise) starting from the original position of South-West, as this position is now the new reference (North) in the transformed system. The original position of South-West is $225^\circ$.
5. Calculate the new direction: $225^\circ$ (South-West) $- 45^\circ$ (counter-clockwise) $= 180^\circ$.
6. The direction corresponding to $180^\circ$ is South.

Therefore, under this Direction Transformation, what was originally North-West becomes South.