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Rotation as Product of Two Reflections

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reflection 1
show
reflection axis
reflection line
reflection 2
show
reflection axis
reflection line
rotation
show
orientation
reset
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This Demonstration shows some of the relationships between composition of reflections and rotation. In particular it shows that a composition of two reflections is equivalent to a rotation. The initial graphic consists of a solid blue asymmetric object
A
(upper right) and three translucent transforms of
A
:
1. a rotation of
A
about the graph origin (green translucency, upper left)
2. a reflection of
A
(magenta translucency, lower right)
3. a reflection of the reflection of
A
(red translucency, lower left)
There are four lines: the axis and action lines of the reflections, colored like their reflections.
By playing with the rotation and reflection sliders you can see that you can align the second reflection with the rotation exactly, showing that a rotation is a composition of two reflections.
You can hide some of the graphical elements to concentrate on certain relationships. You may also note an interesting relationship between the reflection angles and the rotation angle. See the Details section for more information.​
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