Connect with experts and get insightful answers on IDNLearn.com. Ask your questions and receive reliable, detailed answers from our dedicated community of experts.
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
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 value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Find reliable answers at IDNLearn.com. Thanks for stopping by, and come back for more trustworthy solutions.