Translations are rigid transformations that move an object by sliding it sideways, up, down and diagonally, without manipulating the size, shape, or orientation of the object. When translating an object it is important to make sure the size or shape of the object is not effected by the translation. If the object is changed at any point in size or shape it no longer statisfies the definition of a rigid transformation and translation.


Coming up with examples of translations can be tricky as there are not many examples found in nature that hold to the definition of translations however here are some examples that are commonly seen throughout our society: the movement of aircraft as they travel through the sky, a car driving down the highway, sliding a drink across the counter, and moving chess pieces across a chessboard. These examples statisfy the definition of translations as they are moving from one position to another without the objects size or shape being altered.


Plants growing towards the sky or the rising of a cake in the oven are not examples of translations. While these examples may seem like they are traveling from one position to another they are also changing in size and shape, remember translations need to remain rigid and unchanging in shape.


Can you think of some examples or nonexamples of translation you've encountered?

Here is an applet to explore the simplicity of translations. By checking the boxes in the applet circles that can be translated will show.

Can you see anything interesting regarding the transformation from the applet?

Are the circles following the definition of being rigid transformations?

And what do you notice about the x and y values of the ordered pairs labeling the center of the circles?




Here is an additional applet constructed by Ben Graber using the software Geogebra to explore the basic properties of translations.

Do you notice any similarities between this applet and the previous applet?