For a center fed half wave dipole operated at resonance, the voltage and current at the feed point are in phase in time and there is zero reactance present in the impedance seen at the feed point.
For the points in between the center feed point and the ends of the antenna, are the voltage and current also in phase in time ? which would mean that everywhere on the antenna at resonance V and I are in phase and there is no reactance present anywhere ?
This is a different question to :
What is the impedance of an off-center fed resonant dipole?
Which asks how the feed point impedance changes as the feed point is moved away from the center.