Explain the relationships between corresponding parts of the pre-image and image of a dilation. Creating an image by enlarging or reducing a figure is called adilation . The image is the figure resulting from the dilation. The preimage is the original figure. The pre-image and image are similar figures. You can examine the corresponding vertices and corresponding sides to describe a relationship between the pre-image and image of a dilation.

1. Dilations
Algebra
Prepared by
Yousef Elshrek

2. •Dilations
• Mississippi Standard: Explain the relationships between corresponding
parts of the pre-image and image of a dilation.
• Creating an image by enlarging or reducing a figure is called adilation .
• The image is the figure resulting from the dilation.
• The preimage is the original figure.
• The pre-image and image are similar figures.
• You can examine the corresponding vertices and corresponding sides to
describe a relationship between the pre-image and image of a dilation.

3. •Example : Describe a Dilation
• Figure ABCD is dilated to create figure A'B'C'D'.
• Describe how the image changed from the pre-image.
• Examine the corresponding vertices of the pre-image and the
image.
• The vertices of the pre-image, ABCD, were doubled to create the image,
A'B'C'D'.

4. • Examine the lengths of the corresponding sides of the pre-image and
image.
• The sides of the pre-image, ABCD, were doubled to create the image,
A'B'C'D'.
• In Example 1, the vertices and sides of the pre-image were doubled to create
the image.
• Therefore, the scale factor is 2.
• The scale factor refers to the ratio of corresponding parts of similar
figures.
• If the scale factor is greater than 1, the dilation is an enlargement .
• If the scale factor is less than 1, the dilation is a reduction .

5. • Example
• FIND AND CLASSIFY A SCALE FACTOR
• Segment X'Y' is a dilation of segment XY. Find the scale factor of the
dilation and classify it as an enlargement or as a reduction.
• Write a ratio of the x- or y-coordinate of one vertex of the image to the x-
or y-coordinate of the corresponding vertex of the pre-image. Use the
y-coordinates of X(0, 2) and X'(0, 5).
• The scale factor is
• Since the scale factor is greater than
• 1, the dilation is an enlargement.

6. •Exercises
• Describe how the corresponding parts of the image and pre-image are
related.

7. • In each figure, the green figure is a dilation of the blue figure. Find the scale
factor of each dilation and classify it as an enlargement or as a reduction.

8. • 8. GEOMETRY Segment C'D' with endpoints C'(2, 2) and D'(5, 1) is a
dilation
• of segment CD with endpoints C(4, 4) and D(10, 2). Find the scale factor
of
• the dilation, and classify it as an enlargement or as a reduction.
• 9. COMPUTERS Carlos graphed a triangle with vertices A(1, 1), B(1, 3),
and
• C(3, 1) using geometry software. If he enlarges the triangle by a scale
factor
• of 3, what will be the vertices of the dilation?
• 10. PHOTOS To place a photo in a frame, Emma must reduce the photo
by a
• scale factor of 14
• . Find the dimensions of the reduced photo if the original is
• 8 inches by 10 inches.

9. • DESIGN For Exercises 11 and 12, use the following information.
• Dante’s logo design won a competition for creating the logo for the
new town
• library. The logo, which is 4 inches wide and 7 inches long will be
enlarged and
• used on bags for the library. On the bags, the logo will be 10 inches
wide.
• 11. What is the scale factor for this enlargement?
• 12. What will be the length of the logo on the bags?