Question

Select all of the options which are true of the perpendicular bisector of line AB.

It is a fixed distance from line AB
It meets line AB at 90°
It meets line AB at 180°
It passes through A
It passes through B
It does not meet line AB
It passes through the midpoint of line AB

Answer 1

The true statements are:

It is a fixed distance from line AB

It passes through the midpoint of line AB

The perpendicular bisector of a line segment AB possesses distinct geometric properties. Firstly, it is a fixed distance from line AB, equidistant from both endpoints A and B. This characteristic stems from its nature as the locus of points equidistant from A and B. Secondly, the perpendicular bisector passes through the midpoint of line AB, a consequence of its role in dividing the line segment into two equal parts. However, it does not meet line AB at 180°; rather, it intersects the line at a right angle (90°), forming two equal segments.

, the perpendicular bisector does not pass through points A and B, except in special cases where the line AB is a horizontal or vertical line. In summary, the perpendicular bisector combines fixed distance, midpoint intersection, and perpendicularity to line AB, defining its geometric characteristics.