Transcript Honors Geometry Transformations Section 3 Translations and
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
2.
PP
The following coordinate notation can define translations in the coordinate plane: are constants. This notation shifts the
A
D D
C
B
(
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
A
B
2 5 Reflection in the x-axis 90 clockwise about the origin 1 2
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
NO, it is not a glide reflection