Not necessarily. If picture is drawn to scale, no.
Step-by-step explanation:
Line segment EF is certainly perpendicular to line segment AC, but we don't know if it bisects or not.
If the picture isn't drawn to scale, there is no way to know if EF is a perpendicular bisector to AC or not because we do not know if AD = CD.
If the picture is drawn to scale, EF is not a perpendicular bisector to AC because we can see that AD ≠ CD and therefore EF cannot be a perpendicular bisector.
