V by -ing
The 'reciprocate' groupThese verbs are concerned with responding to something that has been done, or compensating for it. The prepositional phrase indicates what someone does in response or as compensation.
This is a productive use. Many other verbs which concern a response to an action or situation sometimes have this pattern. The verbs listed below are the ones which are most frequently used in this way.
atone compensate counter react reciprocate reply respond retaliate retort
After his arrest he was asked if he wanted to say anything. He answered by singing a chorus of We Shall Overcome.
In hot, dry and windy weather, water evaporates from the leaves of plants which in turn compensate by taking more up through their roots.
On Thursday he will reciprocate by entertaining the Queen to a fabulous banquet at the hotel.