What is Translations in Math?

From Latin: translatus - "carried over, "

Moving a figure to a new location with no other changes.

Try this Drag any orange dot to reshape the left (yellow) original figure. Drag any vertex of the image (right, gray) to translate it to a new location.

To translate a figure is to simply slide it somewhere else. But in the move, you may not change the figure in any other way. You cannot rotate it, resize it, or flip it over. You may only slide it side to side, up and down.

In the diagram above, the original object is the yellow one on the left. By translating it up and to the right, we get the gray object on the right. This is called the translated "image" of the original. Notice the vertices of the original are labelled A, B etc. By convention, the corresponding vertices of the image are labelled A' B' etc. The small dash after the letter is called a 'prime' so the vertices are pronounced "A prime, B prime" and so on.

Properties of translated objects

• Line segments linking a vertex in the original to the corresponding vertex in the image are congruent and parallel.

  In the diagram above, click on "show lines" and note that the segment AA' is congruent and parallel to BB' etc.

A way to remember

Things to try

1. In the yellow figure on the left, drag any vertex to reshape it. Note how the translated image on the right changes to match. The image is merely moved, but otherwise matches the original in every respect.
2. Drag any vertex of the gray image on the right. Notice that the image remains an exact copy of the original except for its location on the plane.