lesson goals identify and use reflections in a plane identify reflections in the x-axis and the...
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Lesson 7.2: Reflections
Lesson GoalsIdentify and use reflections in a planeIdentify reflections in the x-axis and the y-axis
ESLRs: Becoming Competent Learners, Complex Thinkers, and Effective Communicators
ESLRs: Becoming Competent Learners, Complex Thinkers, and Effective Communicators
Properties of Reflection
The line over which a preimage is reflected is called the line of reflection or the “mirror line.”
Each point of the preimage will beequidistant to the line of reflection witheach corresponding point of the image.
Properties of Reflection
'PP
When point P is reflected in a line,the line is the perpendicular
P
P’
l 'PPbisector of
Properties of Reflection
When point P is reflected in a lineand P is on the line, then P = P’
PP’
l
Example
A A’(3, 3)(–3, 3)
Line of reflection
Graph the reflection ofeach of the following points in the y-axis
A(-3, 3)B(2, -5)
C(-1, -1) What do you notice about
the coordinates of the preimage and the image?
Example Graph the reflection ofeach of the following points in the x-axis
A(2, 3)
B(-4, -3)
C(2, -1) What do you notice about
the coordinates of the vertices of the preimage and the image?
x
y
y x
Example
in the line .AB
y xGraph the reflection of
3,2A
2, 1B
2,3
'A 1,2
'B
What do you notice about the coordinates of the vertices of the preimage and the image?
Properties of Reflection
If (x,y) is reflected in the y-axis, its image is (–x,y)
If (x,y) is reflected in the x-axis, its image is (x,–y)
If (x,y) is reflected in y = x, its image is (y, x)
Definition
Line of SymmetryA line in which the figure reflects on itself.
Definition
Line of SymmetryA line in which the figure reflects on itself.
Definition
Line of SymmetryA line in which the figure reflects on itself.
Definition
Line of SymmetryA line in which the figure reflects on itself.
Some figures have multiple lines of symmetry
Definition
Line of SymmetryA line in which the figure reflects on itself.
Some figures have no lines of symmetry
Today’s Assignment
p. 407: 1, 2, 18 – 21, 22 – 25, 48
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