A man standing in front of a plane mirror finds his image to be at a distance of 6 metre from himself. The distance of man from the mirror is :

Options

A. 6m
B. 3m
C. 2m
D. 12m

Answer

To solve the problem, we need to determine the distance of the man from the plane mirror based on the information given about the distance between the man and his image.

### Step-by-Step Solution:

1. **Understand the Setup**:
- A man is standing in front of a plane mirror.
- The image of the man is formed in the mirror.

2. **Identify the Distances**:
- Let the distance of the man from the mirror be denoted as \( x \).
- According to the properties of plane mirrors, the distance of the image from the mirror is also \( x \) (the image is formed at the same distance behind the mirror as the object is in front of it).

3. **Total Distance Between Man and Image**:
- The total distance between the man and his image is given as 6 meters.
- Since the image is behind the mirror, the total distance can be expressed as:
\[ \text{Distance between man and image} = x + x = 2x \]

4. **Set Up the Equation**:
- We know from the problem that this total distance is equal to 6 meters:
\[ 2x = 6 \]

5. **Solve for \( x \)**:
- To find \( x \), divide both sides of the equation by 2:
\[ x = \frac{6}{2} = 3 \]

6. **Conclusion**:
- Therefore, the distance of the man from the mirror is \( 3 \) meters.

### Final Answer:
The distance of the man from the mirror is **3 meters**.

---