1. Lesson 9-7 Dilations
Rigor: Dilate figures on and off a coordinate plane, calculate the scale factor of a dilation
Relevance – Optometry, art, graphic design

2. What is a Dilation? A dilation is a transformation that mapsk
A dilation is a transformation that maps
a pre-image onto an image by multiplying
the distance from the center of dilation to
each vertex by a scale factor (k).
Dilation is an ACTION that produces similar figures.
Coordinate notation: (x,y)  (kx, ky)
Scale factor = 𝑖𝑚𝑎𝑔𝑒 𝑙𝑒𝑛𝑔𝑡ℎ 𝑝𝑟𝑒−𝑖𝑚𝑎𝑔𝑒 𝑙𝑒𝑛𝑔𝑡ℎ
The corresponding segments/ lines are parallel to each other

3. Enlargements and Reductions
Reduction: -1 < scale factor < 1
The center of dilation can be inside, outside, or on the figure. The center of dilation determines the position of the image, the scale factor determines the size.

4. EX 1: What is the scale factor
EX 1: What is the scale factor? Is the dilation a reduction or an enlargement?
The image is in blue, and the pre-image is in black.
A) B)

5. k = 2 B) y = x + 4; (x, y)  (1/2x, 1/2y)
EX 2: Graph the image after a dilation about the origin with the given scale factor.
k = B) y = x + 4;
(x, y)  (1/2x, 1/2y)

6. EX 3: An artist is creating a large painting from a photo by dividing the photo into squares and dilating each square by a scale factor of 4.
If the photo is 20cm by 25cm, what is the perimeter of the painting?

7. Negative Scale Factors
If k is negative, the transformation is a composition of a dilation & a 180o rotation about the center of dilation
EX 4: Draw ΔABC and its image
if ΔABC has vertices A(-1,1), B( -3, -1), and C( -1, -2) under the dilation centered at the origin and k = - 2.

8. EX 5: Constructions! Turn to workbook page 405 example 1

9. 9-7 Classwork
Textbook pg 653
Problems: #2 – 12 even, 18, 28, 29

10. Honors: 9-7 Assignments Primary Assignment: Due Friday
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Codes:
Period 2:
Period 4:
Period 6:
Secondary Assignment:
Workbook pg 407 #1 & 3
Textbook pg 653 #7 – 19 odd, 27, 30, 32

11. Standard: 9-7 Assignments
Primary Assignment: Due Monday
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Codes:
Period 1:
Period 5:
Period 7:
Secondary Assignment:
Worbook pg 407 #1 & 3
Textbook pg 653 #7 – 19 odd, 27, 30, 32