Honors Geometry Transformations
Section 3
Translations and Compositions
A translation (or slide) is a
transformation which maps every two
points P and Q in the plane to points
P and Q so that the following
properties are true:
1. PP QQ
2. PP  QQ
The following coordinate notation can
define translations in the coordinate plane:
(x, y)  ( x + a , y + b ) where a and b
are constants. This notation shifts the
point ________________
a units to the right and
_________.
b units up
B
D
A
D
C
( X , Y )  ( X  1, Y  6)
A composition results when two or
more transformations are
performed one after the other.
Example 1: Sketch the image of AB after a
composition of the given rotation and reflection.
2
-5
1
-2
B
A
2
5
1
2
Reflection in the x-axis
90 clockwise about the origin
A
B
While the order of the transformations
affected the final image in the
previous example, that is not the case
with a glide reflection.
A glide reflection is a composition of a
translation and a reflection where the
line of reflection is parallel to the
direction of the translation.
Example 3: Determine the coordinates of
the image of A(4, -2) after the described
composition. Is the composition a glide
reflection?
A 4,2 
Yes, it is a glide
reflection
Example 4: Determine the coordinates of
the image of A(4, -2) after the described
composition. Is the composition a glide
reflection?
A
A7,7 
NO, it is not a
glide reflection