Which of the following is a false statement ?

Options

A. An infinite number of lines can pass through a given point.
B. A unique line can be drawn to pass through two given points.
C. Ray `bar(AB)` = ray `bar(BA)`
D. A ray has one end point

Answer

To determine which of the given statements is false, we will analyze each option based on Euclid's geometry principles.

### Step-by-Step Solution:

1. **Analyze Option A**: "An infinite number of lines can pass through a given point."
- According to Euclid's geometry, from any given point, we can draw lines in infinitely many directions. Therefore, this statement is **true**.

2. **Analyze Option B**: "A unique line can be drawn to pass through two given points."
- In Euclidean geometry, through any two distinct points, there exists exactly one straight line. Thus, this statement is also **true**.

3. **Analyze Option C**: "A line segment has two endpoints and can be indefinitely extended."
- A line segment has two endpoints and is defined as the straight path between those two points. However, a line (not a line segment) can be extended indefinitely in both directions. Therefore, this statement is **false**.

4. **Analyze Option D**: "A line has one endpoint and extends indefinitely."
- This statement refers to a ray, which indeed has one endpoint and extends indefinitely in one direction. Thus, this statement is **true**.

### Conclusion:
After analyzing all the options, we find that:
- Option A: True
- Option B: True
- Option C: False
- Option D: True

The false statement is **Option C**.