Step-by-Step Directional Analysis

To solve this problem, we first determine the standard positions of the clock hands at the given time and then apply the described rotation of the compass.

1. Standard Clock Positions at "Quarter to Three" (2:45)

On a standard clock face where 12 is North, 3 is East, 6 is South, and 9 is West:

• At 2:45, the minute hand points directly at the 9. The standard direction for this is West.
• At 2:45, the hour hand is three-quarters of the way between the 2 and the 3. For simplicity in this type of problem, its position is considered to be pointing at the 3, which is East.

2. Determining the Compass Rotation

The problem states that the minute hand (which should be pointing West) is actually pointing North-East.

To get from West to North-East on a compass, one must rotate 135 degrees clockwise (West to North is 90°, and North to North-East is another 45°).

3. Applying the Rotation to the Hour Hand

We must apply the same 135-degree clockwise rotation to the standard direction of the hour hand to find its new direction.

• The standard direction of the hour hand is East.
• Rotating East by 135 degrees clockwise:
  • East + 90° clockwise = South
  • South + 45° clockwise = South-West

Conclusion

After applying the 135-degree clockwise rotation, the hour hand points in the South-West direction.