Which of the following statements is CORRECT ?

Options

A. For every line l and for every point P not lying on l, there exist a unique line m passing through P and parallel to l.
B. For two distinct point A and B, there exists a third point C lying on the line AB which is in between A and B.
C. A figure formed by the line segments is called a rectilinear figure.
D. All of these

Answer

To determine which of the statements is correct, we will analyze each statement one by one based on Euclid's axioms and definitions.

### Step-by-Step Solution:

1. **Statement 1**: "For every line L and for every point P not lying on L, there exists a unique line M passing through P and parallel to L."
- **Analysis**: According to Euclid's parallel postulate, through a point not on a line, there is exactly one line parallel to the given line. Thus, this statement is **correct**.

2. **Statement 2**: "For two distinct points A and B, there exists a third point C lying on the line A which is between A and B."
- **Analysis**: By the definition of a line segment, if we have two distinct points A and B, we can always find another point C that lies on the line segment connecting A and B. Therefore, this statement is also **correct**.

3. **Statement 3**: "A figure formed by the line segments is called a rectilinear figure."
- **Analysis**: A rectilinear figure is defined as a figure whose edges are formed by straight line segments. This includes shapes like rectangles, squares, and triangles. Thus, this statement is **correct**.

4. **Conclusion**: Since all three statements are correct, the final option "All of these are correct" is also **correct**.

### Final Answer:
All of the statements (1, 2, and 3) are correct, therefore the answer is: **All of these are correct.**

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