The number of line segments detemined by three collinear points is …………. (two, three, only one).

Answer

To determine the number of line segments formed by three collinear points, we can follow these steps:

### Step 1: Understand Collinear Points
Collinear points are points that lie on the same straight line. If we have three points, say A, B, and C, and they are collinear, they all lie on the same line.

**Hint:** Remember that collinear points do not form separate segments; they are all part of the same line.

### Step 2: Identify the Line Segments
A line segment is defined as a part of a line that is bounded by two distinct endpoints. In the case of three collinear points, we can form line segments between the points.

**Hint:** Consider how many pairs of points can be formed from the three points.

### Step 3: Count the Segments
For three points A, B, and C:
- The segment between A and B is one segment.
- The segment between B and C is another segment.
- The segment between A and C is the third segment.

However, since all three points are collinear, they lie on the same line, and we can only consider the entire line segment formed by the outermost points.

**Hint:** Think about how the segments overlap when the points are collinear.

### Step 4: Conclusion
Thus, the number of distinct line segments determined by three collinear points is **one**. This is because all three points are on the same line, and they do not create separate segments.

**Final Answer:** The number of line segments determined by three collinear points is **one**.