April 14, 2011
Bell Ringers - April 8
Graph the reflection of the polygon in the given line.
2. y = x
1. y = 2
A
B
D
C
C
B
A
3. The line y = 2x – 5 is reflected
in the x- axis. What is the
equation of the image?
4. The line y = 3x + 2 is
reflected in the line y = -1.
What is the equation of the
image?
April 14, 2011
9.4 PERFORM ROTATIONS
rotation – a transformation in which a figure is turned about a
fixed point
A rotation about a point P through an angle of xº maps every
point Q in the plane to a point Q' so that one of the following
properties is true:
1. If Q is not the center of rotation P, then
QP = Q'P and m∠QPQ' = xº
R
R'
2. If Q is the center of rotation P,
then the image of Q is Q.
Q'
center of rotation – the fixed point
angle of rotation – angle formed by rays drawn from the
center of rotation to a point and its image
Thm 7.2 Rotation Theorem
A rotation is an isometry
Q
xº
P
April 14, 2011
Ex 1 Rotate the figure 75º clockwise about the point P.
A
B
C
D
P
Ex 2: Rotate the figure 45º clockwise about the point P.
I
J
H
•P
April 14, 2011
A
triangle
has
coordinates
A(‐2,3),
B(0,4),
and
C(3,1).
Rotate
it
180º
clockwise
around
the
origin.
Write
the
coordinates
of
the
new
vertices
using
prime
notation.
Coordinate Rules for Rotations about the Origin
When a point (a, b) is rotated counterclockwise about
the origin, the following are true:
1. For a rotation of 90º:
2. For a rotation of 180º:
3. For a rotation of 270º:
April 14, 2011
Ex
2
A
triangle
has
vertices
W
(2,3),
X
(4,1)
and
Y
(1,6).
Rotate
it
90º
counterclockwise
about
the
origin.
Name
the
coordinates
of
the
new
vertices.
Ex
3 A
triangle
has
coordinates
A(–6,1),
B(–4,4),
and
C(–1,5).
Rotate
it
270º
clockwise
around
the
origin.
What
are
the
coordinates
of
the
new
vertices?
Homework:
Pages 602 - 605 # 1-8, 10, 11, 13, 14, 20-24, 29-33, 36, 37
April 14, 2011
Bell Ringers - April 9
1. Graph the reflection of the
polygon in the given line.
y-axis
2. Graph the reflection of the
polygon in the given line.
y = -x
2
3. The line y = -x + 2 is reflected in the y-axis.
What is the equation of the image?
April 14, 2011
A
triangle
has
vertices
A(‐2,3),
B(0,4),
and
C(3,1).
Rotate
it
90º
counterclockwise
about
the
origin.
Write
the
coordinates
of
the
new
vertices
using
prime
notation.
Coordinate Rules for Rotations about the Origin
When a point (a, b) is rotated counterclockwise about
the origin, the following are true:
1. For a rotation of 90º:
2. For a rotation of 180º:
3. For a rotation of 270º:
April 14, 2011
A
triangle
has
coordinates
A(‐2,3),
B(0,4),
and
C(3,1).
Rotate
it
270º
counterclockwise
around
the
origin.
Write
the
coordinates
of
the
new
vertices
using
prime
notation.
Coordinate Rules for Rotations about the Origin
When a point (a, b) is rotated counterclockwise about
the origin, the following are true:
1. For a rotation of 90º:
2. For a rotation of 180º:
3. For a rotation of 270º:
April 14, 2011
Coordinate Rules for Rotations about the Origin
When a point (a, b) is rotated counterclockwise about
the origin, the following are true:
1. For a rotation of 90º:
2. For a rotation of 180º:
3. For a rotation of 270º:
Ex
3 A
triangle
has
coordinates
A(‐2,3),
B(0,4),
and
C(3,1).
Rotate
it
60º
clockwise
around
the
origin.
What
are
the
coordinates
of
the
new
vertices?
Homework:
Pages 602 - 605 # 1-8, 10, 11, 13, 14, 20-24, 29-33, 36, 37