Answered

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

Sagot :

GinnyAnswer
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
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