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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.
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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.)
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2. |
mapping: |
(This
is read: "the x and y coordinates will be
translated into
x-7 and
y-3".
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 x-coordinates, while
the -3 tells you to subtract 3 from all of your y-coordinates.)
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.) |
|
)
is a transformation of the plane that slides every point of a figure the same
distance in the same direction.
