![Page 1: Dilations in the Coordinate Plane EQ: How do you describe the properties of dilation? How can you describe the effect of dilation on coordinates using](https://reader031.vdocuments.net/reader031/viewer/2022020718/56649d6e5503460f94a4fa9b/html5/thumbnails/1.jpg)
Dilations in the Coordinate Plane
EQ: How do you describe the properties of dilation?
How can you describe the effect of dilation on coordinates using algebraic representation?
What is the connection between transformation and similar figure?
![Page 2: Dilations in the Coordinate Plane EQ: How do you describe the properties of dilation? How can you describe the effect of dilation on coordinates using](https://reader031.vdocuments.net/reader031/viewer/2022020718/56649d6e5503460f94a4fa9b/html5/thumbnails/2.jpg)
Dilations Dilation
A transformation that changes the size of a figure. The original figure and transformed figure are similar.Corresponding angles are sameCorresponding side lengths are not same; but proportional
Center of dilation - The point of projectionIn the coordinate plane, the center of dilation is the origin.
![Page 3: Dilations in the Coordinate Plane EQ: How do you describe the properties of dilation? How can you describe the effect of dilation on coordinates using](https://reader031.vdocuments.net/reader031/viewer/2022020718/56649d6e5503460f94a4fa9b/html5/thumbnails/3.jpg)
The dilation is an enlargement if the scale factor is > 1.
The dilation is a reduction if the scale factor is between 0 and 1.
Two types of dilationsEnlargementReduction
![Page 4: Dilations in the Coordinate Plane EQ: How do you describe the properties of dilation? How can you describe the effect of dilation on coordinates using](https://reader031.vdocuments.net/reader031/viewer/2022020718/56649d6e5503460f94a4fa9b/html5/thumbnails/4.jpg)
Dilations Scale factor - The amount
of change written as a ratio
To find the new coordinates, multiply the original coordinates by the scale factor.
![Page 5: Dilations in the Coordinate Plane EQ: How do you describe the properties of dilation? How can you describe the effect of dilation on coordinates using](https://reader031.vdocuments.net/reader031/viewer/2022020718/56649d6e5503460f94a4fa9b/html5/thumbnails/5.jpg)
Steps to Follow1. Plot the given points.
2. Multiply each coordinate by the scale factor.
3. Plot the image points.
4. State the coordinates of the dilation.
![Page 6: Dilations in the Coordinate Plane EQ: How do you describe the properties of dilation? How can you describe the effect of dilation on coordinates using](https://reader031.vdocuments.net/reader031/viewer/2022020718/56649d6e5503460f94a4fa9b/html5/thumbnails/6.jpg)
Finding a Scale Factor
The blue triangle is a dilation image of the red triangle. Describe the dilation.
The center is X. The image is larger than the preimage, so the dilation is an enlargement.
34
84''
XT
TX
![Page 7: Dilations in the Coordinate Plane EQ: How do you describe the properties of dilation? How can you describe the effect of dilation on coordinates using](https://reader031.vdocuments.net/reader031/viewer/2022020718/56649d6e5503460f94a4fa9b/html5/thumbnails/7.jpg)
Finding a Scale Factor
The blue quadrilateral is a dilation image of the red quadrilateral. Describe the dilation.
![Page 8: Dilations in the Coordinate Plane EQ: How do you describe the properties of dilation? How can you describe the effect of dilation on coordinates using](https://reader031.vdocuments.net/reader031/viewer/2022020718/56649d6e5503460f94a4fa9b/html5/thumbnails/8.jpg)
Graphing Dilation Images ∆PZG has vertices P(2,0), Z(-1, ½), and G (1, -
2).What are the coordinates of the image of P for a dilation with center (0,0) and scale factor 3?
a) (5, 3) b) (6,0) c) (2/3, 0) d) (3, -6)
![Page 9: Dilations in the Coordinate Plane EQ: How do you describe the properties of dilation? How can you describe the effect of dilation on coordinates using](https://reader031.vdocuments.net/reader031/viewer/2022020718/56649d6e5503460f94a4fa9b/html5/thumbnails/9.jpg)
Algebraic Notation of Dilation
In a coordinate plane, dilations whose centers are the origin have the property that the pre-image P to image P’ where ‘k’ is the scale factor.
P (x, y) P’ (kx, ky)
![Page 10: Dilations in the Coordinate Plane EQ: How do you describe the properties of dilation? How can you describe the effect of dilation on coordinates using](https://reader031.vdocuments.net/reader031/viewer/2022020718/56649d6e5503460f94a4fa9b/html5/thumbnails/10.jpg)
4) Algebraic to verbal (2, 3)
a)(x, y) (2x, 2y) __________________
b)New coordinates: ( )
b) (x, y) (1/4x, 1/4y)__________________ New coordinates: ( )
c) (x, y) (2.5x, 2.5y)_____________________
New coordinates: ( )
d) (x, y) (-2y, 2x)_______________________
New coordinates: ( )
![Page 11: Dilations in the Coordinate Plane EQ: How do you describe the properties of dilation? How can you describe the effect of dilation on coordinates using](https://reader031.vdocuments.net/reader031/viewer/2022020718/56649d6e5503460f94a4fa9b/html5/thumbnails/11.jpg)
Given the vertices of the triangle, find a dilation by a scale factor of 3.
A (1,2) B (3,3) C (1,3)
y
x
C B
A
C’B’
A’A’ (3,6)
B’ (9,9)
C’ (3,9)
![Page 12: Dilations in the Coordinate Plane EQ: How do you describe the properties of dilation? How can you describe the effect of dilation on coordinates using](https://reader031.vdocuments.net/reader031/viewer/2022020718/56649d6e5503460f94a4fa9b/html5/thumbnails/12.jpg)
Given the vertices of the rectangle, find a dilation by a scale factor of 2/3.
A (-6,-3) B (-6,3) C (6,3) D (6,-3)
y
x
A
B C
D
A’ (-4,-2)B’ (-4,2)
C’ (4,2)D’ (4,-2)
A’
B’ C’
D’
![Page 13: Dilations in the Coordinate Plane EQ: How do you describe the properties of dilation? How can you describe the effect of dilation on coordinates using](https://reader031.vdocuments.net/reader031/viewer/2022020718/56649d6e5503460f94a4fa9b/html5/thumbnails/13.jpg)
DILATION
Triangle: A (-2, -4)B (3, -2)C (1, 2)D (-4,0)Color Red
Scale factor of 2
Scale factor of
1/2
Scale factor of 3
Algebraic Representation
(x, y) ( )
(x, y) ( )
(x, y) ( )
New Coordinates:
A’ ( )B’ ( )C’ ( ) D’ ( )Color Blue
A’’ ( )B’’ ( )C’’ ( )D”( )Color Green
A’’’ ( )B’’’ ( )C’’’ ( )D’’’ ( )Color Pink