What is a mathematical transformation that moves the origin of a coordinate system?

A mathematical transformation that shifts the origin of a coordinate system is known as a translation. When a translation occurs, every point in the coordinate plane is moved the same distance in a specific direction. This operation effectively changes the position of all points in the plane without altering their relative distances and angles.

In the context of moving the origin, translation can be visualized as shifting the entire graph of a function or a set of points in the x-y plane to a new location, thus establishing a new origin point. For instance, if you are tasked with moving the origin from point (0, 0) to another point, such as (h, k), each point (x, y) would become (x + h, y + k).

This maintains the structure of the figure or graph while relocating it within the coordinate system. In contrast, the other transformations like rotation, reflection, and dilation involve changes to size and orientation rather than simply shifting the entire coordinate system’s origin.