The direction in which the hour hand of a clock points at 1.30 P.M. can be determined by understanding the movement of the hour hand and the minute hand.

1. Understanding the movement of the hour hand:
- The hour hand completes a full revolution around the clock in 12 hours.
- This means that it moves at a rate of 360 degrees in 12 hours.
- Therefore, the hour hand moves 30 degrees per hour (360 degrees divided by 12 hours).

2. Understanding the movement of the minute hand:
- The minute hand completes a full revolution around the clock in 60 minutes.
- This means that it moves at a rate of 360 degrees in 60 minutes.
- Therefore, the minute hand moves 6 degrees per minute (360 degrees divided by 60 minutes).

3. Analyzing the initial position of the minute hand:
- The question states that at 12 noon, the minute hand points towards north-east.
- North-east is a direction halfway between north and east, which is at an angle of 45 degrees clockwise from north.
- Therefore, at 12 noon, the minute hand is pointing at an angle of 45 degrees clockwise from north.

4. Determining the position of the hour hand at 1.30 P.M.:
- From 12 noon to 1.30 P.M., a total of 1 hour and 30 minutes have passed.
- The hour hand moves at a rate of 30 degrees per hour, so in 1.5 hours, it will move 45 degrees (30 degrees multiplied by 1.5).
- Since the hour hand was initially pointing at 12 noon towards north-east (45 degrees clockwise from north), it will move an additional 45 degrees clockwise.
- Therefore, at 1.30 P.M., the hour hand will be pointing at an angle of 90 degrees clockwise from north.

5. Conclusion:
- At 1.30 P.M., the hour hand points at an angle of 90 degrees clockwise from north, which corresponds to the east direction.