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.
Preimage:
the original figure
Image:
the figure after the
transformation
Isometry:
a transformation that does not
change the size or shape of a figure
Which of the transformations are examples of
isometry?
Translations, reflections, and rotations
12-1 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
Holt Geometry
Reflection:
Reflection is a transformation that moves a
figure by flipping it across a line
Reflection
The original figure is called the preimage
and the reflected figure is called the image.
A reflection is the reflected image always
congruent to the preimage?
What do we call this?
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.
Yes; the image appears
to be flipped across a
line.
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.
Yes; the image
appears to be
flipped across a line.
We are going to
reflect images on the
coordinate plane
across given lines 
Reflecting across vertical lines (x = a)
Reflect across x = -2
Step 1 – Draw line of reflection
A
D
B B'
C
C'
A'
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
Do # 3 on your worksheet
Label the coordinates of the preimage.
Reflecting across y-axis
Reflect the following shape across the y-axis
Pre-image
A
B
Image
A(
,
)
A'(
,
)
B(
,
)
B'(
,
)
C(
,
)
C'(
,
)
C
Do # 4 on your worksheet
Label the coordinates of the preimage.
Reflecting across x-axis
Reflect the following shape across the x-axis
Pre-image
A
B
C
Image
A(
,
)
A'(
,
)
B(
,
)
B'(
,
)
C(
,
)
C'(
,
)
Do #5 on your worksheet
Label the coordinates of
the preimage.
Reflecting across the line y = x
Remember:
Move ONLY vertically or horizontally…think about why?
Pre-Image
F
H
F(
,
)
I(
,
)
S(
,
)
S'( , )
H(
,
)
H'( , )
I
S
Image
F'( , )
I'( , )
Do #6 on your worksheet
Label the coordinates of
the preimage.
Look back at the problems you just
completed.
Compare the x and y-coordinates for the
pre-image and image.
Can you see a rule for each reflection?
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.
V
S
U
U’
T
T’
V’
S’
Reflect across y = –x
A
K
C
E
C’(
,
)
A’(
K’(
,
)
E’(
,
,
Do #8 on your worksheet
)
)
Lesson Quiz
Reflect the figure with the given
vertices across the given line.
1. A(2, 3), B(–1, 5), C(4,–1); y = x
A’(3, 2), B’(5,–1), C’(–1, 4)
2. U(–8, 2), V(–3, –1), W(3, 3); y-axis
U’(8, 2), V’(3, –1), W’(–3, 3)
3. E(–3, –2), F(6, –4), G(–2, 1); x-axis
E’(–3, 2), F’(6, 4), G’(–2, –1)