Reflections
What will we accomplish in today’s
lesson?
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Given a pre-image and its reflected image, determine the line of reflection.
Given a pre-image and its reflected image graphed on the coordinate plane,
determine the line of reflection and give a function rule for the reflection.
Given the line of reflection, draw a reflection on plain paper.
Given a horizontal or vertical line of reflection or function rule, draw a
reflection on the coordinate plane.
Reflections
• A reflection is a transformation that flips a figure across a line, called
the line of reflection.
• Segments connecting corresponding points of a pre-image and its
reflected image are bisected by the line of reflection.
• Corresponding points of a pre-image and its reflected image are
equidistant from the line of reflection.
• The reflection of a figure changes orientation so that it faces in the
opposite direction of the original figure.
What is a reflection?
• A reflection is a transformation that flips a figure
over a line called the line of reflection.
• A reflection is a type of rigid transformation.
line of reflection (the x-axis in this example)
Properties of Reflections
• Segments connecting corresponding points
of a pre-image and its reflected image are
bisected by the line of reflection.
Properties of Reflections
• Corresponding points of a pre-image and its
reflected image are equidistant from the line
of reflection.
• The reflection of a
figure changes
orientation so that it
faces in the opposite
direction of the original
figure.
Coordinate notation for reflections in
the coordinate plane
3 rules for reflections in a coordinate plane
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reflection across the x-axis:
(x, y)  (x, -y)
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reflection across the y-axis:
(x, y)  (-x, y)
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reflection across the line y=x:
(x, y)  (y, x)
Reflect the following figure across the x-axis
pre-image points
(1,1)
(4,1)
(4,4)
Reflect the following figure across the y-axis
Reflect the following figure across the line y=x
pre-image points
(-3,2)
(-1,2)
(-1,5)
Options for the line of reflection
• A reflection can occur across any line.
• It is not limited just to the x-axis, y-axis, and
line y=x.
Identifying the equation for the line of reflection helps to see the change
between the coordinates of the pre-image and image.
The line of reflection is represented by the equation x = -2.
To begin, find the distance from the pre-image point to the line of
reflection. Each image point must be that same distance in the opposite
direction from the line of reflection.
For example, point A is 3 units from the line of reflection. So A' must be
three units in the opposite direction from the line of reflection.
Reflect the figure across the line x=2
pre-image points
(1,4)
(1,1)
(0,1)
Reflect the line across y=3
pre-image points
(7,3)
(-1,7)
(1,4)
(6,3)
Try it yourself!
• http://www.shodor.org/interactivate/activi
ties/Transmographer/