In geometry, what does a transformation involving a change in position without altering the object's shape refer to?

The correct answer is a transformation that involves a change in position without altering the object's shape, which is specifically known as a translation.

A translation shifts an object from one location to another on the coordinate plane without changing its size, shape, or orientation. For example, if you move a triangle 3 units to the right and 2 units up, the triangle remains congruent to its original position, retaining all of its properties such as angles and side lengths.

The other types of transformations mentioned also involve changing an object's position but include alterations to its orientation. A rotation, for instance, turns the object around a fixed point, which affects how it is oriented in space but not its shape. Similarly, a reflection flips the object over a line, creating a mirror image, which again changes the object's position and orientation. The term "transformation" is more general and encompasses all types of movements including translations, but specifically referring to a translation highlights the aspect of moving an object without structural changes.