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9.3 – Perform Reflections
Reflection:
Transformation that uses a line like a mirror to reflect an image
Line of Reflection:
Mirror line in a reflection
A reflection in a line m maps every point P in the plane to a point , such that:
• If P is not on m, then m is the perpendicular bisector of
• If P is on m, then
'.PP
'P
'P P=
P
Reflect point P(5, 7) in the given line.
'P
P(5, 7) becomes'(5, 7)P −
A reflection in the x-axis changes (x, y) into _______(x, –y)
x – axis
P
Reflect point P(5, 7) in the given line.
'P
P(5, 7) becomes'( 5, 7)P −
A reflection in the y-axis changes (x, y) into _______(–x, y)
y – axis
P
Reflect point P(5, 7) in the given line.
'P
P(5, 7) becomes'(7, 5)P
A reflection in the y = x changes (x, y) into _______(y, x)
y = x
Graph the reflection of the polygon in the given line.
x – axis
'C
'A
'B
Graph the reflection of the polygon in the given line.
y – axis
'C
'A
'B
'D
'C
'A
'B
Graph the reflection of the polygon in the given line.
y = x
(–1 , –3)
(–3, –1)
A=
'A =
(2, –4 )
(–4, 2)
B =
'B =
(3, 0)
(0, 3)
C =
'C =
Graph the reflection of the polygon in the given line.
x – axis
'C
'A
'B
'D
Graph the reflection of the polygon in the given line.
x = –1
'C'A
'B
Graph the reflection of the polygon in the given line.
y = 2'C
'A =
'B
'D=
9.4 – Perform Rotations
Rotation: Transformation that turns a figure about a fixed point
Center of Rotation:
The point that the rotation happens around
Angle of Rotation:
Degree the figure is rotated counterclockwise
A rotation about a point P through an angle of x° maps every point Q in the plane to a point such that:
'Q
• If Q is not the center of rotation, then and 'QP Q P= 'm QPQ x∠ = °
PQ
'Q
x°
A rotation about a point P through an angle of x° maps every point Q in the plane to a point such that:
'Q
• If Q is the center of rotation, then 'Q Q=
Q 'Q=
1. Match the diagram with the angle of rotation.
B. 90°
1. Match the diagram with the angle of rotation.
A. 30°
1. Match the diagram with the angle of rotation.
C. 150°
State if the rotation is 90°, 180°, or 270° counter-clockwise.
Counter-clockwise degree of rotation: _______180°
State if the rotation is 90°, 180°, or 270° counter-clockwise.
Counter-clockwise degree of rotation: _______90°
State if the rotation is 90°, 180°, or 270° counter-clockwise.
Counter-clockwise degree of rotation: _______270°
6. Find the value of each variable in the rotation.
x = 4
z = 3
y = z + 2y = 3 + 2
y = 5
6. Find the value of each variable in the rotation.
4s = 24
s = 6
r = 2s – 3 r = 2(6) – 3
r = 9
r = 12 – 3
9.3
9.4
593-594
602-605
WS
3-7, 9, 12 (Graph on worksheet)
3-8, 20, 21, 44-46
ROTATION WS
HW Problems
9.3 #7
A'
B'C '
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