12-1 Reflections
Introduction and Review
Information
Holt Geometry
12-1 Reflections
A transformation is a change in the position, size, or
shape of a figure or graph. It is sometimes called a
mapping.
Examples of transformations are: translations,
reflections, rotations, and dilations.
A transformation is an isometry if the size and shape of
the figure stay the same.
Which of the transformations above are an isometry?
Translations, reflections, and rotations
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12-1 Reflections
Every transformation has a preimage and an image.
• Pre-image is the original figure in the
transformation (the “before”). Its points
are labeled as usual.
• Image is the shape that results from the
transformation (the “after”). The points are
labeled with the same letters but with a '
(prime) symbol after each letter.
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12-1 Reflections
Example
Pre-Image
Image
A'
A
B
C
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B'
C'
12-1 Reflections
• Mapping
– A way of showing where you started and
finished a transformation.
– It uses an arrow (→)
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12-1 Reflections
Writing Equations
Remember equations for horizontal lines:
y = 2 is horizontal line crossing y-axis at 2
y = –4 is horizontal line crossing y-axis at 4
y=2
y =–4
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12-1 Reflections
Writing Equations
Remember equations for vertical lines:
x = 2 is vertical line crossing x-axis at 2
x = –4 is vertical line crossing x-axis at –4
x =–4
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x=2
12-1
12-1Reflections
Reflections
I CAN
- Accurately reflect a figure in space.
- Reflect a figure across the x-axis, the y-axis
the line y = x, or the line y = –x
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Geometry
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Geometry
12-1 Reflections
Recall that a reflection is a transformation that
moves a figure (the preimage) by flipping it across
a line.
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12-1 Reflections
Example 1: Identifying Reflections
Tell whether each transformation appears to
be a reflection. Explain.
B.
A.
No; the image does not
Appear to be flipped.
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Yes; the image appears
to be flipped across a
line..
12-1 Reflections
Check It Out! Example 1
Tell whether each transformation appears to
be a reflection.
a.
b.
No; the figure
does not appear to
be flipped.
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Yes; the image
appears to be
flipped across a line.
12-1 Reflections
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12-1 Reflections
Reflecting across vertical lines (x = a)
Refer to “Reflections” Worksheet Example #3
Reflect across x = 2
Step 1 – Draw line of reflection
A
B
B'
A'
D
C
C'
D'
Step 2 – Pick a starting point,
count over-ALWAYS vertically
or horizontally to line
Step 3 – Go that same distance
on the other side of line
Step 4 – LABEL THE NEW POINTS
Step 5 – Continue with other points
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12-1 Reflections
Reflecting across y-axis
Refer to “Reflections” Worksheet Example #4
C
A T’
C’
T A’
Pre-image
Image
C(-3, 7)
C'(3, 7)
A(-3, 2)
A'(3, 2)
T(2, 2)
T'(-2, 2)
What do you notice about
the x and y coordinates
of the pre-image and image
points?
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12-1 Reflections
Reflecting across x-axis
Reflect the following shape across the x-axis
T
H
A
A’
T’
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M
M’
H’
Pre-image
M(2, 1)
A(-1, 1)
Image
M’(2, -1)
A’(-1, -1)
T(-3, 5)
T’(-3, -5)
H(4, 5)
H’(4, -5)
What do you notice about
the x and y coordinates
of the pre-image and image
points?
12-1 Reflections
Reflecting across the line y = x
Refer to “Reflections” Worksheet #6
Pre-Image
I’
S’
F
H
F(-3, 0)
F‘(0, -3)
I(4, 0)
I'(0, 4)
S(4, -9)
S'(-9, 4)
H(-3, -9) H'(-9, -3)
F’
H’
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I
Image
S
What do you notice about
the x and y coordinates
of the pre-image and image
points?
12-1 Reflections
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12-1 Reflections
If time permits, work on problem 8 on “Reflections”
Worksheet.
8. Reflect across y = –x
M(-5, 2)
E
E’
M’
M
V’
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O
O’
V
V(0, 6)
O(-2, 2)
E(-7, 6)
M’(-2, 5)
O’(-2, 2)
V’(-6, 0)
E’(-6, -7)
12-1 Reflections
If time permits, work on problem 7 on “Reflections”
Worksheet.
8. Reflect across y = -3
H’(-12, 2)
H
T
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A’(7, -7)
A
T’(2, -7)
12-1 Reflections
Check It Out!
Reflect the rectangle with vertices S(3, 4),
T(3, 1), U(–2, 1) and V(–2, 4) across the x-axis.
The reflection of (x, y) is (x,–y).
S(3, 4)
S’(3, –4)
T(3, 1)
T’(3, –1)
U(–2, 1)
U’(–2, –1)
V(–2, 4)
V’(–2, –4)
Graph the image and preimage.
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V
S
U
U’
T
T’
V’
S’
12-1 Reflections
Lesson Quiz
Reflect the figure with the given vertices
across the given line.
3. A(2, 3), B(–1, 5), C(4,–1); y = x
A’(3, 2), B’(5,–1), C’(–1, 4)
4. U(–8, 2), V(–3, –1), W(3, 3); y-axis
U’(8, 2), V’(3, –1), W’(–3, 3)
5. E(–3, –2), F(6, –4), G(–2, 1); x-axis
E’(–3, 2), F’(6, 4), G’(–2, –1)
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