Unit 404 Vocabulary Dilation A transformation in which a figure is made larger or smaller with respect to a point called the center of dilation Example The red polygon has been Dilated ID: 265163
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Slide1
Transformations: Dilation
Unit 4.04Slide2
Vocabulary
Dilation:
A transformation
in which a figure is made larger or smaller with respect to a point called the center of dilation.
Example: The red polygon has been Dilated (made larger) to form the blue polygon.Slide3
Vocabulary
Center of Dilation:
The point from which a figure is dilated. When graphed on the Cartesian Plane, the Origin is often the Center of Dilation.
Example:
Here, the Origin (0, 0) is the Center of Dilation.
Center of Dilation (0, 0)Slide4
Vocabulary
Scale Factor:
In a dilation, the original figure and dilated image are similar. The ratio that compares the one with the other is called the
Scale Factor
and is called k.Example: The blue square is twice the size of the red
square.
If
red
blue
, then what is the scale factor?
What if
blue
red?
k =
2
k
= ½Slide5
Vocabulary
Dilation on the Cartesian Plane:
To dilate a figure in respect to the origin,
multiply
the coordinates of each vertex by the scale factor, k.Slide6
Vocabulary
Dilation on the Cartesian Plane:
To dilate a figure in respect to the origin,
multiply
the coordinates of each vertex by the scale factor, k.Transformation Notation of Dilations: (x, y) (kx,
ky
)
Classifying a Dilation by the Scale Factor:
When
k > 1,
the dilation is an
enlargement
When 0 < k < 1,
the dilation is a
reductionSlide7
Vocabulary
Example 1:
Dilate ΔABC by the scale factor
,
k = 3, then classify it.Slide8
Vocabulary
Example 2:
Dilate Rectangle WXYZ by the scale factor,
k
= ½ (or 0.5), then classify it.Slide9
You Try It!Slide10
1
)
Dilate ΔABC by a scale factor, k = 2, then classify it.
(1,3)
A: _____________B: _____________C: ____________A’: ____________B’: ____________C’: ____________(4,0)(-3,-2)(2,6)
(8,0)
(-6,-4)
A
B
C
A
’
B
’
C
’Slide11
2
)
Dilate ΔXYZ by a scale factor, k = 1/3, then classify it.
(3,9)
X: _____________Y: _____________Z: _____________X’: ____________Y’: ____________Z’: ____________(9,0)(-3,-3)
(1,3)
(3,0)
(-1,-1)
X
Y
Z
X’
Y’
Z’Slide12
3
)
Dilate
ΔJKL by a scale factor, k= 2.
Then translate it down 5 and to the right 5 units.KLJK’
L’
J’
J’: ____________
K’: ____________
L’: ____________
J
’’: ___________
K
’’: ___________
L
’’: ____________
(-1,-2)
(2,1)
(-5,3)
(-2,-4)
(4,2)
(-10,6)
J
: ____________ K: ____________ L: ____________
(3,-9)
(9,-3)
(-5,1)
K’’
L’’
J’’Slide13
Homework Time
Scale It! -- Dilations WS