reciprocate

Concise Oxford English Dictionary © 2008 Oxford University Press:
reciprocate /rɪˈsɪprəkeɪt/

▶verb

• 1 respond to (a gesture or action) with a corresponding one.

  ■ return (love, affection, etc.) to someone who gives it.

• 2 (usu. as adj. reciprocating) (of a machine part) move backwards and forwards in a straight line.

– derivatives
reciprocation noun,
reciprocator noun.

– origin C16: from L. reciprocat-, reciprocare, from reciprocus (see reciprocal).