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DilationDilationDilationDilationPage 7Page 7
DilationDilationDilationDilation
• Write down one or two examples of how DILATIONS (scaling) are used in cartography (mapmaking), model building, or some other field?
?
Dilation – increasing or decreasing the size of an object according to a scale factor.
Notation Example: D2Scale factor = 2
Multiply the x and y coordinates by the scale factor.
-3D(3,1) 1. .Ex
2
1D
(4,-6) 2. .Ex
(-2,4) of image thefind to)55()( rule the Use3. . yx,x,yEx
)3,9(
)3,2(
)20,10(
RULE: kDy)(x, ky)(kx,
In 1-4, use the rule (x,y)→(4x,4y) to find the image of:
(7,0) .3)5,3( .1
)4,4(),( yxyx )20,12(
In 5-8, find the image of the given point under a dilation of 5.
(-9,-7) .7)1,2( .5
D 5
)0,28(
)5,10()35,45(
In 9-12, Find the image using D-3(x,y) = (-3x,-3y).
)1,6( .9 )3,18(
In 13-18, Write a single rule for a dilation so the image of A is A’.
)20,8(')5,2( .19
)9,6(')6,4( .17
)2,5(')4,10( 5.1
)10,4(')5,2( .13
AA
AA
AA
AA
3D)8,3( .11 )24,9(
3D
2D
2
1D
2
3D
4D
Think of 2 ways to come up with the scale factor
),), C(,), B(,A(-ABCwExample
431013 with Δon 2 offactor scale aith dilation thePerform :
)4,3(
)1,0(
)1,3(
C
B
A )2,6(' A
)2,0('B
)8,6('C
'A
'B
'C
You can check by extending a line from the origin through A to A’
yxyx 2,2,
)0,2(
)2,2(
)2,1(
)3,3(),(
C
B
A
yxyx
)6,3('A
)6,6('B
)0,6('C
'A'B
'C
)2,4(
)4,6(
)4,0(
2
1,
2
1),(
N
E
H
yxyx
)2,0('H
)2,3('E
)1,2(' N
'H
H E
N
'E
'N
.a
'H
H E
N
'E
'N
3'' 6 EHHE.b
1:2
'': EHHE.c
Area.d
bhA NEH 2
1'''
5.4332
1'''
NEH
A
Area.d
bhAHEN 2
1
18662
1
HENA
1:4
: ''' NEHHEN AA.e
Homework
• Page 7: 2-20 evens, 33AB
In 1-4, use the rule (x,y)→(4x,4y) to find the image of:
(-4,9) .4
)2,3( .2
)4,4(),(
yxyx
)8,12(
In 5-8, find the image of the given point under a dilation of 5.
(0,-8) .8
)20,12( .6
D 5
)36,16(
)100,60()40,0(
In 9-12, Find the image using D-3(x,y) = (-3x,-3y).
)0,4( .10 )0,12(
In 13-18, Write a single rule for a dilation so the image of A is A’.
)6,8(')9,12( .20
)6,8(')3,4( .18
)2,5(')8,20( 6.1
)7,21(')1,3( .14
AA
AA
AA
AA
3D)1,10( .12 )3,30(
3D
7D
4
1D
2D
32
D
)3,1(
)0,0(
)2,1(
3,3),(
G
O
H
yxyx
)6,3('H
)0,0('O
)9,3('G
'H
'G
'O
.a
