Question

Answer the questions about a segment in a plane:

A. How many midpoints does the segment have?
B. How many bisectors does it have?
C. How many lines in the plane are its perpendicular bisectors?
D. How many lines in space are its perpendicular bisectors?

Answer 1

1. A segment can have only 1 midpoint.
2. The bisector divides the segment into two equal parts. Thus, there are infinite number of lines that can be a bisector to the given segment. The lines differ only in orientation.
3. There is only 1 among the bisector that is perpendicular to the segment.
4. There are infinite perpendicular bisectors in the space.

Answer 2

The correct answers are:

A) 1

B) infinitely many

C) 1

D) infinitely man

Step-by-step explanation:

A) On any given line segment, there is exactly one point that splits it into two separate segments.

B) There are infinitely many bisectors of a segment, all of which can bisect the segment at different angles.

C) There is only 1 perpendicular bisector; out of the infinitely many bisectors, only one will intersect at a 90° angle.

D) There are infinitely many in 3 dimensional space. This is because there is a plane normal to the line segment (perpendicular to) that goes through the point; there are an infinite number of lines in a plane, so that gives us infinitely many perpendicular bisectors of the segment.