A concept of online trajectory generation for robot motion control systems that enables instantaneous reactions to unforeseen sensor events was introduced in a former publication. This concept is now extended with the important feature of homothety. Homothetic trajectories are 1-D straight lines in a multidimensional space and are relevant for all straight-line motion operations in robotics. This paper clarifies 1) how online concepts can be used to generate homothetic trajectories and 2) how we can instantaneously react to (sensor) events with homothetic trajectories. To underline the practical relevance, real-world experimental results with a seven-degree-of-freedom (DOF) robot arm are shown.