Reflections

Report
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Real-life reflections
Animation
Architecture
Graphic Design
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Reflections
 A reflection creates a mirror image of each point of a
figure.
• A reflection is a transformation, an operation that
changes a figure into another figure. The new
figure created is called the image.
• Notation: A A' is read
“A goes to A prime”.
A' •
4
•A
3
2
1
-2 -1 0
1
2
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Reflection
 Tell whether the red figure is a reflection of the blue figure.
This figure is a reflection.
This figure is not a reflection.
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Reflections
 A reflection is a transformation in which a figure is
flipped over a line of reflection. This line can be
thought of as a mirror in which the image is a
reflection of the pre-image.
 For this class, our line of reflection will be either the
x-axis or the y-axis on a coordinate grid.
Reflecting a Polygon
1.
2.
3.
4.
5.
Determine the line of reflection (x or y axis).
Find the distance from the vertex of the polygon to
the line of reflection.
Mark the image of the vertex the same distance from
the line of reflection, but in the opposite direction.
Continue steps 2-3 until all vertices have been
reflected.
Draw the image by drawing line segments
connecting adjacent vertices.
Example
Reflecting in the y-Axis
Preimage
Image
Coordinates of each
vertex of the triangle and
its image.
Pre-image
Image
(-3, -2)
(-10, 0)
(-2, 3)
(3, -2)
(10, 0)
(2, 3)
Notice that when a point is reflected over the y-axis,
its x-coordinate is multiplied by -1.
http://staff.argyll.epsb.ca/jreed/math9/strand3/transformations.htm
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Reflecting in the x-Axis
Coordinates of each vertex of
the triangle and its image.
Pre-image
(-2, 2)
(-1, 7)
(6, 5)
Image
(-2, -2)
(-1, -7)
(6, -5)
Notice that when a point is reflected over the x-axis, its
y-coordinate is multiplied by -1.
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Conjecture
 A proposition or conclusion that is based on limited
evidence.
 Example: Bats have wings and can fly. Eagles have
wings and can fly. A Pegasus has wings and can fly.
Conjecture: Any animal with wings can fly.
Reflections
 Reflection across the x-axis
 Words
To reflect a point across the x-axis, multiply its
y-coordinate by -1.
Pre-image Image
Algebra
(x, y)
(x, -y)
 Reflection across the y-axis
 Words
To reflect a point across the y-axis, multiply its
x-coordinate by -1.
Algebra
Pre-image
Image
(x, y)
(-x, y)
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Your turn!
Graph the triangle with
vertices J(0, 1), K(1, 4), and
L( 5, 2). Reflect the triangle
in the y-axis.
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Your turn!
Graph the quadrilateral
with vertices S(-3,2),
T(-1, 4), U(-4, 5), and
V(-5, 3). Reflect the
quadrilateral in the x-axis.
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