Question

The perpendicular bisector of a line segment is perpendicular to the segment that divided it into how many equal parts?
A) Three
B) Two
C) Four
D) None of the above

Answer 1

Hint: In the above question, we are given a perpendicular bisector of a line segment. We have to determine that in how many equal parts the perpendicular bisector that is perpendicular to that line segment divides that line segment. In order to approach the solution, we have to first define a perpendicular bisector.

Complete step by step answer:
Given that, a perpendicular bisector of a line segment.
We have to find that in how many equal parts the perpendicular bisector that is perpendicular to that line segment divides that line segment.
Now let us define a perpendicular and a bisector separately.
A perpendicular to a line segment is a line that makes a right angle to the given line segment, such as the two sides opposite to the hypotenuse in a right angled triangle.
Whereas a bisector of a line segment is a line that divides the given line segment into two equal parts, such as the two diagonals of a parallelogram.
Combining both of these properties in a single line, we call it the perpendicular bisector of a given line segment.
Therefore, a perpendicular bisector of a line segment is defined as the perpendicular line to the line segment that divides the line segment into two equal parts, such as the two diagonals of a square or a rhombus, since they make right angle with each other as well as divide each other into two equal parts.
Therefore, the correct answer is “C. Two”.

Note:
A line segment can have infinitely many perpendiculars as well as bisectors but the perpendicular bisector of a line segment is unique.

Here, AB is a line segment whose mid point is O.
ROS is the bisector of AB whereas PQ is a perpendicular to AB.
But the perpendicular bisector of AB is unique, that is MON.