Which interface allows computer users to drag images and documents across their monitor?

The Graphical User Interface (GUI) is the correct answer because it is designed to enable users to interact with a computer through visual elements such as icons, buttons, and windows. One of the key features of a GUI is the ability to use a mouse or other pointing device to drag images and documents across the screen. This visual representation makes it easier for users to understand and navigate their files and software applications.

In contrast, the Command Line Interface (CLI) operates through text input and requires users to type commands without visual representation, making dragging and dropping impossible. The Application Programming Interface (API) serves as a way for different software applications to communicate with each other programmatically, but it does not deal with user interaction at the level where dragging occurs. Lastly, the Text-Based User Interface (TUI) allows for interaction through text but lacks the visual components necessary for dragging and dropping elements on a monitor. Therefore, the GUI is specifically designed to facilitate these user-friendly actions, making it the ideal choice for this question.