The number of perpendiculars bisectors that can be drawn of a given line segment is :

Options

A. 0
B. 1
C. 2
D. infinitely many.

Answer

To solve the question about the number of perpendicular bisectors that can be drawn of a given line segment, we will follow these steps:

### Step-by-Step Solution:

1. **Understanding the Line Segment**:
- Consider a line segment \( AB \). A line segment is defined by two endpoints, \( A \) and \( B \).

2. **Defining the Midpoint**:
- The midpoint \( O \) of the line segment \( AB \) is the point that divides the segment into two equal parts. It can be found using the formula:
\[ O = \frac{A + B}{2} \]
- This midpoint is unique for any given line segment.

3. **Understanding the Perpendicular Bisector**:
- A perpendicular bisector is a line that is perpendicular (forms a right angle) to the line segment and passes through the midpoint.
- Since the midpoint \( O \) is unique, there can only be one line that is perpendicular to \( AB \) at point \( O \).

4. **Conclusion**:
- Therefore, there can only be **one** perpendicular bisector for any given line segment \( AB \).

### Final Answer:
The number of perpendicular bisectors that can be drawn of a given line segment is **1**.