Lesson: Transformations P T
There are 4 major types of transformations
There are 4 major types of transformations
Rotations
There are 4 major types of transformations
Rotations
Reflections
There are 4 major types of transformations
Rotations
Reflections
Translations
There are 4 major types of transformations
Rotations
Reflections
Translations
Dilations
How many major types of transformations are there?
Translations are just shifts
Translations are just shifts
up
Translations are just shifts
up
Up 6
Translations are just shifts
up, down
Translations are just shifts
up, down
Down 5
Translations are just shifts
up, down, left
Translations are just shifts
up, down, left
Left 3
Translations are just shifts
up, down, left, and right
Translations are just shifts
up, down, left, and right
right 4
Sometimes translations can be written like this
Sometimes translations can be written like this
(x+3,y+2)
Sometimes translations can be written like this
(x+3,y+2)
This means
Sometimes translations can be written like this
(x+3,y+2)
This means
a right translation of 3
Sometimes translations can be written like this
(x+3,y+2)
This means
a right translation of 3
Sometimes translations can be written like this
(x+3,y+2)
This means
and
a right translation of 3
an up translation of 2
Sometimes translations can be written like this
(x+3,y+2)
This means
and
a right translation of 3
an up translation of 2
Moving the point 4 places to the right
Moving the point 4 places to the right
Moving the point 4 places to the right
is a plus 4 to the x value
Moving the point 4 places to the right
is a plus 4 to the x value
(x+4, y)
Moving the point 4 places to the left
Moving the point 4 places to the left
Moving the point 4 places to the left
is a subtraction of 4 from x
Moving the point 4 places to the left
is a subtraction of 4 from x
(x-4, y)
(x+3, y)
Right 3
?
Left 3
?
(x-3, y)
Moving the point 4 places up
Moving the point 4 places up
is an addition of 4 to the y
Moving the point 4 places up
is an addition of 4 to the y
(x, y+4)
Moving the point 4 places down
Moving the point 4 places down
Moving the point 4 places down
is a subtraction of 4 from the y
Moving the point 4 places down
is a subtraction of 4 from the y
(x, y-4)
Check all that apply
(x-5, y-12)
Right
Up
Down
Left
Check all that apply
(x-3, y+1)
Right 3
Right 1
Left 3
Left 1
Down 1
Up 3
Up 1
Down 3
Check all that apply
(x+8, y+4)
Right 8
Right 4
Left 8
Left 4
Down 4
Up 8
Up 4
Down 8
Which point is the
Point A translated:
correct answer?
(x-2, y+1)
H
G
I
F
A
B
E
D
C
Right 2, Up 4
Left 1, Up 4
(x+2, y+4)
?
(x-1, y+4)
?
Match the translation
Right 7, Down 3
Left 3, Up 2
(x-3, y+2)
?
(x+7, y-3)
?
Left 2, Down 1
Left 7, Up 3
(x-7, y+3)
?
(x-2, y-1)
?
A reflection flips the point over a line
Translation
Reflection
Shifts
?
Flips
?
A reflection flips the point over a line
A reflection flips the point over a line
A y axis reflection
A reflection flips the point over a line
A y axis reflection
would flip the point
over the y axis
A reflection flips the point over a line
A y axis reflection
would flip the point
over the y axis
A reflection flips the point over a line
A y axis reflection
So it is the same distance
would flip the point
on both sides
over the y axis
A reflection flips the point over a line
2
A y axis reflection
So it is the same distance
would flip the point
on both sides
over the y axis
A reflection flips the point over a line
2
A y axis reflection
So it is the same distance
2
would flip the point
on both sides
over the y axis
A reflection flips the point over a line
An x-axis reflection
flips over the x-axis
A reflection flips the point over a line
An x-axis reflection
flips over the x-axis
A reflection flips the point over a line
So that the point is the
An x-axis reflection
same distance from the 
flips over the x-axis
x-axis
A reflection flips the point over a line
3
So that the point is the
An x-axis reflection
same distance from the 
flips over the x-axis
x-axis
A reflection flips the point over a line
3
3
So that the point is the
An x-axis reflection
same distance from the 
flips over the x-axis
x-axis
Which point is point A reflected across the y-axis?
Which point is point A reflected across the x-axis?
A
C
B
A reflection across the x axis also changes the 
sign of the y value
A reflection across the x axis also changes the 
The point (-2, 3) reflected across the x axis would be
sign of the y value
A reflection across the x axis also changes the 
The point (-2, 3) reflected across the x axis would be
sign of the y value
(-2, -3)
A reflection across the x axis also changes the 
The point (-2, 3) reflected across the x axis would be
sign of the y value
(-2, -3)
Notice the sign of the y changes
A reflection across the y axis changes the sign of the x
The point (2,-3) reflected across the y axis would be
A reflection across the y axis changes the sign of the x
The point (2,-3) reflected across the y axis would be
(-2, -3)
A reflection across the y axis changes the sign of the x
Notice the change in x
The point (2,-3) reflected across the y axis would be
(-2, -3)
Point (-1,4) reflected across the y axis
Point (-5,3) reflected across the x axis
Point (5,7) reflected across the x axis
(5,
(
(
,4)
,
)
)
A rotation is a turn
Reflection
Rotation
Translation
Turn
?
Shift
?
Flip
?
In order to turn a point
It is helpful to use the "L" shape.
In order to turn a point
It is helpful to use the "L" shape.
In order to turn a point
It is helpful to use the "L" shape.
In order to turn a point
It is helpful to use the "L" shape.
In order to turn a point
It is helpful to use the "L" shape.
or you could draw the "L" like this
In order to turn a point
It is helpful to use the "L" shape.
or you could draw the "L" like this
To rotate the point 90 clockwise, turn the 'L'
To rotate the point 90 clockwise, turn the 'L'
To rotate the point 90 clockwise, turn the 'L'
To rotate the point 90∘ counter clockwise,
turn the 'L' the other way
To rotate the point 90∘ counter clockwise,
turn the 'L' the other way
To rotate the point 90∘ counter clockwise,
turn the 'L' the other way
turn the 'L' twice
To rotate the point 180,
turn the 'L' twice
To rotate the point 180,
once
turn the 'L' twice
To rotate the point 180,
twice
Point A rotated 180
C
B
D
A
Point A rotated 90 clockwise
C
B
D
A
Point A rotated 90 counter clockwise
C
B
D
A
A dilation enlarges or reduces an object.
A dilation enlarges or reduces an object.
We can use the "L" method again.
A dilation enlarges or reduces an object.
We can use the "L" method again.
A dilation enlarges or reduces an object.
We can use the "L" method again.
A dilation enlarges or reduces an object.
We can use the "L" method again.
To enlarge by a factor of 2
just double the sides of 
the L
A dilation enlarges or reduces an object.
We can use the "L" method again.
To enlarge by a factor of 2
just double the sides of 
the L
A dilation enlarges or reduces an object.
We can use the "L" method again.
4
2
To enlarge by a factor of 2
just double the sides of 
the L
A dilation enlarges or reduces an object.
We can use the "L" method again.
4
8
2
To enlarge by a factor of 2
just double the sides of 
the L
A dilation enlarges or reduces an object.
We can use the "L" method again.
4
8
2
4
To enlarge by a factor of 2
just double the sides of 
the L
A dilation enlarges or reduces an object.
We can use the "L" method again.
4
8
2
4
To enlarge by a factor of 2
just double the sides of 
the L
A dilation enlarges or reduces an object.
We can use the "L" method again.
This is my new point
4
8
2
4
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