Transformations Preimage +
rotation  
Pre Image
An operation that maps (moves) a preimage to  an
image is a transformation.  This transformation is a:
reflection
translation
Image
Pre Image
?
This is a tranSLation (SLide) to the right.
The NEW figure is the image.
Image
?
This is a tranSLation (SLide) to the left.
The NEW figure is the image.
Image
?
Pre Image
?
If the preimage has point A
A
The image has corresponding (matching) point  A'
B
C
A'
B'
?
C'
?
If the preimage has point A, the image has point A'.
A' is read as "A prime"
A
PREIMAGE
?
B
C
A'
IMAGE
?
B'
C'
If the                 has point A, the image has point A'.
A' is read as "A           "
preimage
preimage
C
?
prime
A
B
image
C'
A'
?
B'
?
2
-2
4
-4
2
-2
4
-4
6
-6
A
C
B
C'
A'
B'
Coordinate notation
shows this translation
(x,y)→(x+2, y-5)
This means the
preimage moves
2 units right
and 5 units down
to form the image
2
-2
4
-4
6
-6
2
-2
4
-4
6
-6
8
-8
10
-10
(x,y)→(x+2, y-7)
(x,y)→(x-2, y+7)
(x,y)→(x-2, y-7)
(x,y)→(x+2, y+7)
Which coordinate
notation is shown?
A'
A
B'
C'
B
C
2
-2
4
-4
6
-6
2
-2
4
-4
6
-6
8
-8
10
-10
(x,y)→(x+2, y-7)
(x,y)→(x-2, y+7)
(x,y)→(x-2, y-7)
(x,y)→(x+2, y+7)
Which coordinate
notation is shown?
A
A'
B
C
B'
C'
2
-2
4
-4
6
-6
2
-2
4
-4
6
-6
8
-8
10
-10
(x,y)→(x+2, y-7)
(x,y)→(x-2, y+7)
(x,y)→(x-2, y-7)
(x,y)→(x+2, y+7)
Which coordinate
notation is shown?
A
A'
C
B
B'
C'
2
-2
4
-4
6
-6
2
-2
4
-4
6
-6
8
-8
10
-10
(x,y)→(x+2, y-7)
(x,y)→(x-2, y+7)
(x,y)→(x-2, y-7)
(x,y)→(x+2, y+7)
Which coordinate
notation is shown?
A'
A
C'
B'
B
C
RECAP
The
process
of mapping
(moving)
a
preimage
onto an
image
is called a:
preimage
transformation
prime
 coordinate notation
(x,y)→(x+4,y-3)
What type of notation
describes this translation
(slide)?
prime
coordinate
image
preimage
#
units to the
(x,y)→(x+4,y-3)
This coordinate notation
shows a translation
left
or
right
and         units
#
up
or
down
#
units to the
(x,y)→(x-2, y+7)
This coordinate notation
shows a translation
left
or
right
and         units
#
up
or
down
Final Question.............
Use the coordinate notation to  find the
coordinates of the image. (Let x=5 and y=1 and solve)
(5,1)→(   -2,   +7)
(5,1)→(       ,      )
(x,y)→(x-2, y+7)
Preimage
5
?
Image
1
?
The
End
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