Final answer:
HP is the likely perpendicular bisector of AE since H is the midpoint of AE, and the line segment connecting H to anywhere on AE would be the only option presented that can act as a perpendicular bisector.
Step-by-step explanation:
The question involves understanding the properties of midpoints and perpendicular bisectors in geometry. Given H is the midpoint of AE, and because HM, MP, and GC are cited as line segments, we need to identify which one is the perpendicular bisector of AE. A perpendicular bisector is a line which divides another line segment into two equal parts at a 90-degree angle.
Since H is the midpoint of AE, for any line to be the perpendicular bisector of AE, it would have to pass through H and be perpendicular to AE. Among the options given, HM is part of AE and cannot be perpendicular to it. MP seems to be related to midpoints but its relation to AE is not mentioned. GC is suggested as the midpoint of MP, implying it is not on AE and its perpendicularity to AE is not confirmed. The only remaining option is HP, which, by process of elimination, could entail segment HP starts at H (the midpoint of AE) and is perpendicular to it, making HP the perpendicular bisector.