Answer :
To determine whether a line segment may have more than one midpoint, consider the following steps:
1. Definition of a Midpoint:
- The midpoint of a line segment is a point that divides the segment into two equal parts.
2. Uniqueness of the Midpoint:
- For any given line segment defined by two endpoints, [tex]\( A \)[/tex] and [tex]\( B \)[/tex], the midpoint [tex]\( M \)[/tex] is calculated such that it is equidistant from both [tex]\( A \)[/tex] and [tex]\( B \)[/tex]. This means [tex]\( M \)[/tex] is the single point that satisfies this criterion.
3. Implications of Multiple Midpoints:
- If a line segment had more than one midpoint, there would be multiple points equidistant from [tex]\( A \)[/tex] and [tex]\( B \)[/tex] along the segment. However, in Euclidean geometry, it’s impossible for more than one distinct point to exactly divide a line segment into two equal parts.
Given these considerations, it is clear that a line segment can only have one unique midpoint.
Therefore, the correct answer is:
○ B. False
1. Definition of a Midpoint:
- The midpoint of a line segment is a point that divides the segment into two equal parts.
2. Uniqueness of the Midpoint:
- For any given line segment defined by two endpoints, [tex]\( A \)[/tex] and [tex]\( B \)[/tex], the midpoint [tex]\( M \)[/tex] is calculated such that it is equidistant from both [tex]\( A \)[/tex] and [tex]\( B \)[/tex]. This means [tex]\( M \)[/tex] is the single point that satisfies this criterion.
3. Implications of Multiple Midpoints:
- If a line segment had more than one midpoint, there would be multiple points equidistant from [tex]\( A \)[/tex] and [tex]\( B \)[/tex] along the segment. However, in Euclidean geometry, it’s impossible for more than one distinct point to exactly divide a line segment into two equal parts.
Given these considerations, it is clear that a line segment can only have one unique midpoint.
Therefore, the correct answer is:
○ B. False
