At 12 o'clock, the minute hand is point East. At 4:30, in which direction will the hour hand point?

Options

A. North-west
B. South-east
C. South
D. South-west

Answer

To solve the problem of determining the direction the hour hand points at 4:30, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Initial Position**:
At 12:00, both the hour hand and the minute hand are at the same position, which is pointing East.

2. **Identifying the Positions of the Hands**:
- The minute hand moves 360 degrees in 60 minutes, which means it moves 6 degrees per minute.
- The hour hand moves 360 degrees in 12 hours, which means it moves 30 degrees per hour.

3. **Calculating the Position of the Minute Hand at 4:30**:
- At 4:30, the minute hand is at the 6 on the clock.
- Since each number on the clock represents 30 degrees (360 degrees / 12 hours), the minute hand at 6 is at:
\[ 6 \times 30 = 180 \text{ degrees} \]
- This means the minute hand points West.

4. **Calculating the Position of the Hour Hand at 4:30**:
- At 4:00, the hour hand is at:
\[ 4 \times 30 = 120 \text{ degrees} \]
- From 4:00 to 4:30, the hour hand moves an additional:
\[ \frac{30 \text{ degrees}}{60 \text{ minutes}} \times 30 \text{ minutes} = 15 \text{ degrees} \]
- Therefore, at 4:30, the hour hand is at:
\[ 120 + 15 = 135 \text{ degrees} \]

5. **Determining the Direction of the Hour Hand**:
- The hour hand at 135 degrees is between 120 degrees (which points South-East) and 150 degrees (which points South-West).
- Thus, the hour hand at 4:30 points South-West.

### Final Answer:
The hour hand at 4:30 points in the South-West direction.

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