What is the transformation rule for a translation of coordinates?

In the context of coordinate transformations, a translation involves moving a point from one location to another in a plane without changing its orientation or size. The transformation rule for translation specifically requires adding a constant value (the translation vector) to the original coordinates.

When translating a point, say from a point ((x, y)) to a new location by adding integers (a) and (b), the new coordinates will be ((x + a, y + b)). This means you take the original coordinates and add specific integers to each coordinate, which corresponds directly to the concept of translation.

This understanding is crucial because it clarifies that translation does not alter the points' relationships or create any form of scaling or reflection. The movement is purely additive based on the vector defining the translation, confirming that the operation is straightforward and systematic. The other options, such as scaling, changing the sign of coordinates, or switching coordinates, do not represent the nature of translation correctly.