Download Composition of Transformations

Composition of
Transformations
Transformational Geometry
Definition
• A composition of transformations is a
combination of two transformations in which the
first transformation produces and image and the
second transformation is performed on that
image.
• Example:
A’ is the image of A under a reflection in the line
y=x followed by the translation T2,0, we write:
T2,0 ᵒ ry=x (A) = A’
Glide Reflection
• A glide reflection is a composition of
transformations that consists of a line reflection
and a translation in the direction of the line of
reflection performed in either order.
• distance, angle measure, and midpoint are
preserved.
Example of Glide Reflection
• The point A’(-4, 5) is the image of A under a
glide reflection that consists of a reflection in
the x-axis followed by the translation T-2,0.
What are the coordinates of A?
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Example – Composition of
Transformations
• Find the image of A(3,-2) under the composition
of transformations T-1,4 ◦ ry=x
Example – Composition of
Transformations
• The vertices of triangle DEF are D(3,2), E(5,5),
and F(4,-1).
• If T-3,0 ◦ rx-axis ( DEF) = D’E’F’, find the
coordinates of the vertices of D’E’F’.