Section 9.2:
Reflections
A reflection (flip) creates a mirror image of a figure.
• Each point in the image is the same distance from the line as the original point.
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Reflection Example:
Reflection Rules:
t
Reflect across the x­axis: ___________________
A and A' are both 6 units from line t.
B and B' are both 6 units from line t.
C and C' are both 3 units from line t.
A
A'
Reflect across the y­axis: ___________________
B
C
C'
B'
Each vertex in ABC is the same distance from line t as the vertices in A'B'C'.
Reflect across y = x. _______________________
1
What do you notice about the coordinates when you reflect across the y­axis?
y
A
Tap box for coordinates
B
B'
D
A (­6, 5)
B (­4, 5)
C (­4, 1)
D (­6, 3)
A'
D'
C
C'
x
Example 2: What do you predict about the coordinates when you reflect across the x­axis?
Tap box for coordinates
y
A' (6, 5)
B' (4, 5)
C' (4, 1)
D' (6, 3)
A
D
C'
D'
A'
B'
So (x, y) (­x, y) when you reflect across the y­
axis.
y
Rule: (x, y) (y, x)
A
B
D
C
A' (­6, ­5)
B' (­4, ­5)
C' (­4, ­1)
D' (­6, ­3)
C
When you reflect across the y­axis, the x­coordinate becomes the opposite.
Example 3: Reflect the figure across the line y = x.
A (­6, 5)
B (­4, 5)
C (­4, 1)
D (­6, 3)
B
14
x
When you reflect across the x­axis, the y­coordinate becomes the opposite.
So (x, y) (x, ­y) when you reflect across the x­
axis.
The graph to the right represents a reflection over the ____________.
A x­axis
B
y­axis
C origin
x
D y = x
2
15
17
The graph to the right represents a reflection over the ____________.
16
The graph to the right represents a reflection over the ____________.
A x­axis
A x­axis
B y­axis
B
C origin
C origin
D y = x
D y = x
The rule for reflecting across the x­axis is (x, y) (­x, y).
True
False 18
y­axis
The rule for reflecting across y = x is (x, y) (y, x).
True
False 3
19
The rule for reflecting across the y­axis is (x, y) (­x, y).
True
Example 1: Reflect the figure across the x­axis.
y
A
False D
Example 2: Reflect the figure across the y­axis.
B
C
x
Reflect the figure across the line y = 4.
y
y
B
A
B
C
F
A
D
C
E
x
x
4
Reflect the figure across the line x = ­2.
20
y
The reflection below represents a reflection across:
A
the x axis
C
the x axis, then the y axis
B
the y axis
D
the y axis, then the x axis
B
Pull
y
C
A
A
A
E
x
D
B
C
B'
x
C'
A'
21
The reflection below represents a reflection across:
A
the x axis
B
the y axis
C
y = x
false, it's a rotation
D
22
Describe the reflection below:
A
across the line y = x
C
across the line y = ­3
B
across the y axis
D
across the x axis
A
B
B'
C'
y
D
D'
C'
E'
B'
Pull
y
B
C
x
C
A'
x
A
E
D'
A
D
A'
5
23
Describe the reflection below:
A
across the line y = x
C
across the line y = ­3
B
across the x axis
D
across the line x = 4
Pull
y
D
A'
A
B
B'
x
C
C'
6