Question

Answer the questions about a segment in a plane:

Answer 1

The correct answers are:

A) 1

B) infinitely many

C) 1

D) infinitely man

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.

Answer 2

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.