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Chapter 7 Notes
Mrs. Myers – Geometry
Name ______________________________
Period ______
7.1 Rigid Motion in a Plane



Preimage = the _________________ figure.
Image = ____________ figure.
Transformation = the operation that maps or moves the preimage onto the image.
o 3 Types:
1. Reflection in a line:
2. Rotation about a point:
3. Translation:
Ex. 1 Name the transformation from point A (preimage) to B, C, and D.
* Isometry = is a transformation that preserves lengths, angle measurements, parallel
lines, and distances between points (  )  Rigid Transformations.
*
ABC is mapped onto DEF

ABC  DEF 
Ex. 2 Which transformation is isometries?
A)
7
7
B)
C)
48
45
Ex. 3 GHJ is mapped onto UVW . The mapping is a translation and
GHJ  UVW is isometry. Find GH and m V .
H
V
37
8
71. 5
G
J
U
5
W
Ex. 4 Find each variable if the transformation is isometry.
8y -6
B
K
42
A
J
18
3z
101
D
C
L
2x+19
M
7.2 Reflections
* Theorem 7.1: A reflection is an _________________________.

Line of Symmetry: If the figure can be mapped onto itself. (looks the same on
both sides of the “mirror”).
Ex. 1 Determine the number of lines of symmetry
Ex. 2 Draw the reflection on the
A) y-axis
B) x-axis
2
Preimage
-5
5
-2
7.3 Rotations

Rotation = a figure is turned about a ________________ ________________.

Center of a Rotation = fixed point.
* Theorem 7.2: A rotation is an ______________________.
Ex.1 A quadrilateral has vertices P 3, 1 , Q  4,0 , R  4,3 , and S  2, 4 . Rotate
PQRS 180 counterclockwise about  0, 0  . What are the new vertices?
* Theorem 7.3: The angle of rotation is 2x where x is the measure of the acute or
right angle formed by K and M.
m BPB  2 x
where
AB & AB
(mirror images )
AB & AB (mirror images )
Ex. 2 Describe the transformation that maps RST to RS T 
7.4 Translation

Translation = is a transformation that maps every two points P and Q in the plane
to points P and Q so the following is true:
o PP  QQ
o
*
PP QQ
 x, y  with a shift of  a, b 
Gives us:
 x  a, y  b 
where
a  shift ________________
b  shift ________________
Ex. 1 What is the translation that makes ABC onto ABC  ?
B
2
Image
A
C
-5
5
B
-2
Peimage
A
C
-4
Ex.2 Match the graphs with the description of the translation.
1.
 x, y    x  2, y  3
2.
 x, y    x  3, y  2
3.
 x, y    x  2, y  3
Ex.3 Consider the translation that is defined by the coordinate notation
 x, y    x  4, y  6
A) What is the image of  5, 2  ?
B) What is the preimage of  2,  4  ?

Vector: is a quantity that has both __________________ (north, south, east, west)
and magnitude (___________).

Initial Point: _______________ point (written first)

Terminal Point: _______________ point (written last)
o Example: PQ (vector PQ)



 x1 , y1 
Terminal point = Q  x2 , y2 
Initial point = P
Component Form: x2  x1 , y2  y1
Ex.4 Given the initial point of a vector is V (-2,3) and the terminal point is W (-4, -7).
Name the vector and write its component form.