http://www.ck12.org Chapter 12. Rigid Transformations
12.5 Reflections
Here you’ll learn what a reflection is and how to find the coordinates of a reflected figure.
What if you noticed that a lake can act like a mirror in nature? Describe the line of reflection in the photo below. If
this image were on the coordinate plane, what could the equation of the line of reflection be? (There could be more
than one correct answer, depending on where you place the origin.) After completing this Concept, you’ll be able to
answer this question.
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Guidance
Atransformationis an operation that moves, flips, or changes a figure to create a new figure. Arigid transfor-
mationis a transformation that preserves size and shape. The rigid transformations are: translations, reflections
(discussed here), and rotations. The new figure created by a transformation is called theimage. The original figure
is called thepreimage. Another word for a rigid transformation is anisometry. Rigid transformations are also
calledcongruence transformations. If the preimage is A, then the image would be labeled A′, said “a prime.” If
there is an image of A′, that would be labeled A′′, said “a double prime.”
Areflectionis a transformation that turns a figure into its mirror image by flipping it over a line. Another way to
describe a reflection is a “flip.” Theline of reflectionis the line that a figure is reflected over. If a point is on the line
of reflection then the image is the same as the original point.
Common Reflections
- Reflection over they−axis:If(x,y)is reflected over they−axis, then the image is(−x,y).
- Reflection over thex−axis:If(x,y)is reflected over thex−axis, then the image is(x,−y).