What defines the locus of a single line?

The locus of points that are equidistant from a given line is indeed represented by one parallel line. When we consider a single line in a plane, every point that is the same distance away from this line will form a new line that runs parallel to the original line. This means that for any given point on the parallel line, if you drop a perpendicular to the original line, the distance from that point to the original line remains constant.

This concept is rooted in the definition of a locus, which is a set of points that satisfy certain conditions. In this case, the condition is maintaining a constant distance from the reference line. Thus, as you draw points that are the same distance away from the original line, they create a line that is congruent and parallel to it.

In contrast, other choices do not describe a singular or consistent locus formed relative to a single line. Two parallel lines represent two distinct lines rather than the locus of points related to just one, a perpendicular bisector pertains to the unique location equidistant from two endpoints, and two intersecting lines do not create a constant distance scenario around a single line. Each of these scenarios has its unique geometric interpretation but does not adhere to the definition of a locus created by equ