## Geometry and Trigonometry## Measurements and Transformations |

## What are some transformations in geometry? |

A transformation that keeps a figure’s same shape and size, but moves it to a new location, is called *isometry.* There are several common types of these transformations. *Dilatation* is the only transformation that does not create equal figures. It means to take a shape and make it larger or smaller, but keep the same proportions. In terms of a circle, a dilatation creates another circle with the same center, also known as a concentric circle. *Reflection* is similar to what we called a “flip” in elementary school mathematics—like the flip side of an object. One easy way to see this is by noting one’s reflection in a mirror—the “figure” is on one side of a line and the mirror image on the other. Reflection twice about two parallel lines is synonymous with translation; reflection twice about two intersecting lines is called rotation.

Another type of transformation is *rotation.* This is simple to understand: in elementary school mathematics it is sometimes called a “turn” or “spin.” In this case, one point on a plane remains unchanged while keeping all the distances between the other points the same. Finally, a *translation* (or glide transformation) is similar to what is called a “slide” in elementary school mathematics. All the points in the plane move in the same direction and the same distance; or, the figure slides in a single direction. Translation is also considered to be reflection twice across two parallel lines.