
a.
To identify the invariant under the composite of reflection.
a.

Answer to Problem 13WE
The only property which is invariant under the composite of reflection and dilation is
Explanation of Solution
Given a composite of reflection and dilation.
Calculation:
Check whether the distance varies under a composite of reflection and a dilation or not.
As the composite of two isometries is an isometry, but under dilation , the distance does depend on the scalar factor.
Thus the distance varies under the composite of reflection and dilation.
b.
To identify the invariant under the composite of reflection.
b.

Answer to Problem 13WE
The only property which is invariant under the composite of reflection and dilation is
Explanation of Solution
Given a composite of reflection and dilation.
Calculation:
Check whether the
As the composite of two isometries is an isometry, and transformations, dilation and reflection,
The angle measure does not changes therefore, angle measure is invariant under the composite of reflection and dilation.
c.
To identify the invariant under the composite of reflection.
c.

Answer to Problem 13WE
The only property which is invariant under the composite of reflection and dilation is
Explanation of Solution
Given a composite of reflection and dilation.
Calculation:
Check whether the area varies under a composite of reflection and a dilation or not .
As the composite of two isometries is an isometry, but under dilation, the area does depend on
The scalar factor therefore, area varies under the composite of reflection and dilation.
Chapter 14 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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