Quadrilateral
The quadrilateral undergoes a dilation centered at the origin of scale factor
Watch This
First watch this video to learn about graphs of dilations.
CK12 Foundation Chapter10GraphsofDilationsA
Then watch this video to see some examples.
CK12 Foundation Chapter10GraphsofDilationsB
Guidance
In geometry, a transformation is an operation that moves, flips, or changes a shape to create a new shape. A dilation is a type of transformation that enlarges or reduces a figure (called the preimage) to create a new figure (called the image). The scale factor, r, determines how much bigger or smaller the dilation image will be compared to the preimage.
In order to graph a dilation, use the center of dilation and the scale factor. Find the distance between a point on the preimage and the center of dilation. Multiply this length by the scale factor. The corresponding point on the image will be this distance away from the center of dilation in the same direction as the original point.
If you compare the length of a side on the preimage to the length of the corresponding side on the image, the length of the side on the image will be the length of the side on the preimage multiplied by the scale factor.
Example A
Line
Solution:
Example B
The diamond
Solution:
Example C
The diagram below undergoes a dilation about the origin to form the dilation image. Find the coordinates of
Solution:
Concept Problem Revisited
Test to see if the dilation is correct by determining the scale factor.
Vocabulary
 Center Point
 The center point is the center of the dilation. You use the center point to measure the distances to the preimage and the dilation image. It is these distances that determine the scale factor.
 Dilation
 A dilation is a transformation that enlarges or reduces the size of a figure.
 Scale Factor

The scale factor determines how much bigger or smaller the dilation image will be compared to the preimage. The scale factor often uses the symbol
r .
 Image
 In a transformation, the final figure is called the image.
 Preimage
 In a transformation, the original figure is called the preimage.
 Transformation
 A transformation is an operation that is performed on a shape that moves or changes it in some way. There are four types of transformations: translations, reflections, dilations and rotations.
Guided Practice
1. Line
2. The polygon below has undergone a dilation about the origin with a scale factor of
3. The triangle with vertices
Answers:
1.
2.
3.
Practice
 Dilate the above figure by a factor of
12 about the origin.  Dilate the above figure by a factor of
2 about point D.
 Dilate the above figure by a factor of
3 about the origin.  Dilate the above figure by a factor of
12 about point C.
 Dilate the above figure by a factor of
12 about the origin.  Dilate the above figure by a factor of
12 about point C.
 Dilate the above figure by a factor of
12 about the origin.  Dilate the above figure by a factor of
14 about point C.
 Dilate the above figure by a factor of
12 about the origin.  Dilate the above figure by a factor of
2 about point A.
 Dilate the above figure by a factor of
2 about the origin.  Dilate the above figure by a factor of
12 about point D.
 Dilate the above figure by a factor of
12 about the origin.  Dilate the above figure by a factor of
3 about point D.
 Dilate the above figure by a factor of
12 about the origin.  Dilate the above figure by a factor of
12 about point C.