12-1 Reflections
Introduction and Review
Information
Holt Geometry
12-1 Reflections
Example
Pre-Image
Image
A'
A
B
C
Holt Geometry
B'
C'
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
Holt Geometry
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
Holt Geometry
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
Holt
Geometry
Holt
Geometry
12-1 Reflections
Recall that a reflection is a transformation that
moves a figure (the preimage) by flipping it across
a line.
Holt Geometry
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.
Holt Geometry
Yes; the image appears
to be flipped across a
line..
12-1 Reflections
Holt Geometry
12-1 Reflections
Reflecting across vertical lines (x = a)
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
Holt Geometry
12-1 Reflections
Reflecting across y-axis
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?
Holt Geometry
12-1 Reflections
Reflecting across x-axis
Reflect the following shape across the x-axis
T
H
A
A’
T’
Holt Geometry
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
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’
Holt Geometry
I
Image
S
What do you notice about
the x and y coordinates
of the pre-image and image
points?
12-1 Reflections
Holt Geometry
12-1 Reflections
8. Reflect across y = –x
M(-5, 2)
E
E’
M
V’
Holt Geometry
M’ V
O
O’
V(0, 6)
O(-2, 2)
E(-7, 6)
M’(-2, 5)
O’(-2, 2)
V’(-6, 0)
E’(-6, -7)
12-1 Reflections
8. Reflect across y = -3
H’(-12, 2)
H
T
Holt Geometry
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.
Holt Geometry
V
S
U
U’
T
T’
V’
S’