Which JavaScript application programming interface (API) allows for the creation and manipulation of 2-D images?

The JavaScript API that allows for the creation and manipulation of 2-D images is the Canvas API. This API is part of the HTML5 specification and provides a means to draw graphics via JavaScript. It enables developers to create complex visual elements, including images, shapes, and animations directly within the web browser without needing any plugins.

The Canvas API works through an HTML <canvas> element, where you can use JavaScript methods to draw, manipulate images, render text, and create animations. This makes it a powerful tool for web developers who want to incorporate rich graphics into their applications, including game development, data visualizations, and interactive animations.

The other options do not provide functionality specifically for 2-D image manipulation. The Application Cache is related to offline application storage, Geolocation deals with retrieving the geographical location of a user, and Drag and Drop facilitates dragging items within web applications. None of these elements involve direct creation or manipulation of 2-D graphics in the way that the Canvas API does.