
A
translation "slides" an object
a fixed distance in a given direction. The original object and its translation have the
same shape and size, and they face
in the same direction. A translation creates a figure that
is congruent with the original
figure and preserves distance (length) and orientation
(lettering order). A translation is a
direct isometry.

Translations in the Coordinate Plane:
In the example below,
notice how each vertex moves the same distance
in the same direction.
In
this next example, the "slide" (translation) moves the figure
7 units to the left and 3 units down.
There are several ways to indicate that a translation
is to occur:
1. 
description: 
7 units to the left and 3 units down.
(A verbal description of the
translation is given.)

2. 
mapping: 
(This
is read: "the x and y coordinates will be
translated into
x7 and
y3".
Notice that adding a negative value (subtraction), moves the image left
and/or down, while adding a positive value moves the image
right and/or up.) 
3. 
notation: 
(The
7 tells you to subtract 7 from all of your xcoordinates, while
the 3 tells you to subtract 3 from all of your ycoordinates.)
This may also be seen as
T_{7,3}(x,y)
= (x 7,y  3). 
4. 
vectors: 
(A vector, a directed line segment, may also be used to show the
movement of a translation. See more
about vectors and translations.) 
