Explanation of how the hour and minute hand of a clock make a 90-degree angle at 4 and 7:

Relative positions of the hour and minute hands:
- At 4 o'clock, the hour hand will be pointing directly at the 4 and the minute hand will be pointing at the 12.
- At 7 o'clock, the hour hand will be pointing directly at the 7 and the minute hand will be pointing at the 12.

Understanding the angle between the hands:
- The hour hand moves at a slower pace than the minute hand.
- In the time between 4 and 7 o'clock, the hour hand will move closer to the 5 while the minute hand will move closer to the 12.
- This movement creates a 90-degree angle between the hands when the hour hand is near the 5 and the minute hand is still at the 12.

Visual representation of the 90-degree angle:
- Imagine a right-angled triangle where the hour hand is the adjacent side, the minute hand is the hypotenuse, and the angle between them is 90 degrees.
- At 4 o'clock, the hour hand is the adjacent side as it points towards the 4, while the minute hand is the hypotenuse pointing towards the 12.
- As the hour hand moves towards the 5 and the minute hand stays at the 12, the 90-degree angle between them is formed.

Conclusion:
By understanding the relative positions and movements of the hour and minute hands on a clock between 4 and 7 o'clock, it becomes clear how they can create a 90-degree angle. This concept is essential in understanding the geometry of clock hands and can be visually represented as a right-angled triangle.