Transformations: Translations MathBitsNotebook.com Terms of Use   Contact Person: Donna Roberts

 Translations are SLIDES!!

 A translation moves ("slides") an object a fixed distance in a given direction without changing its size or shape, and without turning it or flipping it. • The original object is called the pre-image, and the translation is called the image. • The image is usually labeled using a prime symbol, such as A'B'C'. • Translations may be described by their movement, such as 5 units to the right and 2 units down.
• An object and its translation have the same shape and size, and face in the same direction.
• In Latin, the word "translate" means "carried across".

Translations can be seen, in a variety of situations:
 (←) Translations can be seen in nature. The hexagonal sections of a honeycomb are the same size, the same shape and face in the same direction. (→) As you go down a slide, you are undergoing a translation. You are moving a given distance in a given direction. You do not change your size, shape or the direction in which you are facing (hopefully!). Certain patterns of musical notes are often repeated (translated) within a composition. The artist M. C. Escher continually used translations, reflections, and rotations in his famous art works. To see the works of M. C. Escher, visit http://www.msescher.com. Seats in a stadium are the same size, the same shape, and face in the same direction.

Translations in the coordinate plane:
Translation 6 units right:

Notice how each vertex moves the same distance in the same direction. All three vertices (A, B and C) are moved 6 units horizontally to the right.

If you move horizontally 6 units to the right, 6 is added to the x-coordinate of each of the vertices.

 Translation 6 units to the right. (x, y) → (x + 6, y)

6 units left, 3 units up:

Be sure you notice where the original figure, ABCD, is located. In this graph, ABCD is on the right.

Each vertex of ABCD is moved 6 units to the left, and then 3 units up.

 Translation 6 units left and 3 units up. (x, y) → (x - 6, y + 3)

 For calculator help with transformations click here.

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