transformations: dilation
DESCRIPTION
Transformations: Dilation. Unit 4.04. 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. Vocabulary. - PowerPoint PPT PresentationTRANSCRIPT
Transformations: Dilation
Unit 4.04
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.
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)
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 = 2k = ½
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.
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
reduction
Vocabulary Example 1: Dilate ΔABC by the scale
factor, k = 3, then classify it.
Vocabulary Example 2: Dilate Rectangle WXYZ by the
scale factor, k = ½ (or 0.5), then classify it.
You Try It!
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’
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’
3) Dilate ΔJKL by a scale factor, k= 2. Then translate it down 5 and to the right 5 units.
KL
J
K’
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’’
Homework Time Scale It! -- Dilations WS