Dive into the world of knowledge and get your queries resolved at IDNLearn.com. Our experts provide prompt and accurate answers to help you make informed decisions on any topic.

Question 1 of 10
A line segment may have more than one midpoint.
○ A. True
B. False


Sagot :

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
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.