Raadha places her clock so that at 1:30 PM., the hour hand points South-West. In which direction will the minute hand point at 4:30 PM ?

1. At 1:30 PM, the minute hand points exactly towards the 6 o'clock position (South), and the hour hand is exactly midway between 1 and 2, which normally corresponds to the North-East direction.
2. The problem states that at this time, the hour hand points South-West. Since South-West is exactly opposite ($180^{\circ }$ rotation) to North-East, the entire clock setup is inverted by $180^{\circ }$.
3. At 4:30 PM, the minute hand is again exactly at the 6 o'clock position, which normally points South.
4. Applying the $180^{\circ }$ inversion rotation to the normal South direction gives North.

Therefore, the minute hand will point North at 4:30 PM.