Which type of line is defined as being composed of points equidistant from the endpoints it divides?

The correct choice describes a perpendicular bisector. A perpendicular bisector is a unique type of line that not only bisects a segment, meaning it divides it into two equal parts at its midpoint, but also does so while intersecting the segment at a right angle (90 degrees).

To understand this more clearly, consider a line segment with two endpoints. The perpendicular bisector creates two segments of equal length, ensuring that any point located on this line is equidistant from both endpoints. This property makes it ideal for constructions and proofs in geometry.

In contrast, a generic bisector could refer to any line that divides an object, but it may not maintain the right angle characteristic. Other options like intersecting lines and transversals do not fulfill the requirement of being equidistant from two specific points, as they either cross at various angles or have a different functional role altogether in geometry.