ma 08 transformations 2.3 reflections. 10/7/20152.3 reflections2 topic/objectives reflection...
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MA 08 transformations
2.3 Reflections
04/19/23 2.3 Reflections 2
Topic/Objectives
Reflection Identify and use reflections in a
plane. Understand Line Symmetry
Essential Question: How can you reflect over a line?
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ReflectionA reflection in line m is a transformation that maps every point P in the plane to point P’ so the following properties are true:
Line of Reflection
m
P P’
P and P’ are equidistant from line m.
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Reflections on the Coordinate Plane
Graph the reflection of A(2, 3) in the x-axis.
3
3
A’(2, -3)
A(2, 3) A’(2, -3)
A Reflection in the x-axis has the mapping:
(x, y) (x, -y)
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Reflections on the Coordinate Plane
Graph the reflection of A(2, 3) in the y-axis.22
A’(-2, 3)A(2, 3) A’(-2, 3)
A Reflection in the y-axis has the mapping:
(x, y) (-x, y)
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Reflections on the Coordinate Plane
Graph the reflection of A(1, 4) in the line y = x.
A’(4, 1)
A(1, 4) A’(4, 1)
A Reflection in the line y = x has the mapping:
(x, y) (y, x)
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Reflection Mappings In the x-axis: (x, y) (x, -y) In the y-axis: (x, y) (-x, y) In y = x: (x, y) (y, x)
We say: Reflect in the x-axis, reflect over the x-axis, reflect on the x-axis, reflect across the x-axis. They mean the same thing.
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Reflect RST in y-axis.
R
S
T
Determine coordinates.
Mapping Formula:
(x, y) (-x, y)
R(0, 4) R’(0, 4)
S(-4, 1) S’(4, 1)
T(-1, -2) T’(1, -2)
(0, 4)
(-4, 1)
(-1, -2)T’(1, -2)
S’(4, 1)
R’(0, 4)
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Reflect ABCD in the x-axis.
Mapping Formula:
(x, y) (x, -y)
A(-2, 2) A’(-2, -2)
B(-3, -1) B’(-3, 1)
C(3, -1) C’(3, 1)
D(2, 2) D’(2, -2)
A(-2, 2)
B(-3, -1) C(3, -1)
D(2, 2)
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Reflect AB on the line x = 2.
A(1, 3)
B(0, 1)
A’(3, 3)
B’(4, 1)