All about Transformations

Transformations are changes  in position or

orientation of a figure.  Types of transformations

include translations - slides along a straight line,

reflections - flips over a line of reflection, rotations -

turns on a fixed point.

 

 

Transformations are

changes in position or orientation of a figure

slides along a straight line

flips overs a line of reflection

turns around a fixed point

Transformations are changes  in position or

orientation of a figure.  Types of transformations

include translations - slides along a straight line,

reflections - flips over a line of reflection, rotations -

turns on a fixed point.

 

 

Translations are

changes in position or orientation of a figure

slides along a straight line

flips overs a line of reflection

turns around a fixed point

Transformations are changes  in position or

orientation of a figure.  Types of transformations

include translations - slides along a straight line,

reflections - flips over a line of reflection, rotations -

turns on a fixed point.

 

 

Reflections are

changes in position or orientation of a figure

slides along a straight line

flips overs a line of reflection

turns around a fixed point

Transformations are changes  in position or

orientation of a figure.  Types of transformations

include translations - slides along a straight line,

reflections - flips over a line of reflection, rotations -

turns on a fixed point.

 

 

Rotations are

changes in position or orientation of a figure

slides along a straight line

flips overs a line of reflection

turns around a fixed point

scale factor

dilations

coordinates

Dilations are  transformations that change the size

but not the shape.  This is done by multiplying

the coordinates of each point by the same number. 

This number is called a scale factor.

 

Changes is size but not shape are called

scale factor

dilations

coordinates

Dilations are  transformations that change the size

but not the shape.  This is done by multiplying

the coordinates of each point by the same number. 

This number is called a scale factor.

 

The number each coordinate is multiplied by is

called a(n)

translation

dilation 

reflection

rotation

reflection

translation

rotation

dilation

reflection

translation

rotation

dilation

Give the coordinates for a 
reflection over the x-axis.
A(4, -3) 
A'(       ,       )
Give the coordinates for a translation using 
the following rule:  (x - 5, y + 4)
W(3, -7)
W'(       ,       )
Give the coordinates of the point when dilated 
using a scale factor of 6.
B(-2, 0)
B'(       ,       )
Give the coordinates for the triangle when
reflected over the y-axis.
A(6, -2)

B(5, -9)

C(8, -4)
A'(        ,        )
B'(        ,        )
C'(        ,        )
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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