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Reflections and Reflective Symmetry
The
most familiar type of symmetry is
reflective
symmetry
(also known as
bilateral symmetry) which results from the transformation called
reflection.
Reflections occur across a line called the
axis.
To reflect a shape across an axis is to plot a special
corresponding point for every point in the original shape.
Specifically, the corresponding point is the point that is the
same distance from the axis as is the original point. You
determine the distance from a point to a line by drawing a line
perpendicular to the original line and that passes through the
point.
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A simple reflection of a point (red) across
an axis to form another point (blue). The
dotted line is the perpendicular line used
to find distances. Notice that the distance
from the red point to the axis is the same
as the distance from the blue point to the
axis.
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Here are several
examples of reflections applied to entire shapes, not just a
single point. The original shape together with its reflection is
said to have reflective symmetry.
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Examples of reflections and reflective
symmetry
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A intuitive way to
think about reflective symmetry is to imagine the turning of the
pages of a book. Suppose you could see through the pages of a
book. Then, when you turn a page, the part that would show
through would be the reflection of the original part.
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How to visualize reflective symmetry
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What does it mean for
a tessellation to have reflective symmetry? If we can perform a
reflection to a tessellation that such that the result is the
same as the original tessellation, then the tessellation has
reflectional symmetry. An
example is as follows:
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A tessellation that has reflective symmetry;
the red dotted line indicates one of the
possible axes of reflection, and the gray
lines are the reflections of the black
lines.
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Real examples of reflective symmetry:
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Line of Symmetry |
Sample Artwork |
Example Shape |
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