Start working on Monday

1
Opening

• Start working on Mondays warm-ups (the colored
  paper on the table).

2
Math 8Day 10

• Learning Target
• Students can define what a dilation is and the
  process.
• 1. Dilations
• 2. Scale Factor

3
Dilations
4
What is a Dilation?

• Dilation is a transformation that produces a
  figure similar to the original by proportionally
  shrinking or stretching the figure.

Dilated PowerPoint Slide
5
Proportionally
Lets take a look
And, of course, increasing the circle increases
the diameter.

• When a figure is dilated, it must be
  proportionally larger or smaller than the
  original.

So, we always have a circle with a certain
diameter. We are just changing the size or scale.
We have a circle with a certain diameter.
Decreasing the size of the circle decreases the
diameter.

• Same shape, Different size.

6
Which of these are dilations??
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Scale Factor and Center of Dilation

• When we describe dilations we use the terms scale
  factor and center of dilation.
• Scale factor
• Center of Dilation

Here we have Igor. He is 3 feet tall and the
greatest width across his body is 2 feet.
He wishes he were 6 feet tall with a width of 4
feet.
His center of dilation would be where the length
and greatest width of his body intersect.
He wishes he were larger by a scale factor of 2.
8
The Object and the Image

• The original figure is called the object and the
  new figure is called the image.
• The object is labeled with letters.
• The image may be labeled with the same letters
  followed by the prime symbol.

Image
Object
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Determining Scale Factor

•  

10
Scale Factor Facts

• If the scale factor is larger than 1, the figure
  is enlarged.
• If the scale factor is between 1 and 0, the
  figure is reduced in size.

Scale factor gt 1
0 lt Scale Factor lt 1
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Ratio Fraction Decimal Percentage Reduction or Enlargement
 12 1/2  .5 50 Reduction
  3/4      
    0.9    
      400  
25        
  1/8      
12
Are the following enlarged or reduced??
C
A
Scale factor of 1.5
D
Scale factor of 3
B
Scale factor of 0.75
Scale factor of 1/5
13
Dilations Used Everyday
14
Remember

• Dilations are enlargements or reductions.
• What are some things that you would not
• mind dilating to make larger or smaller?
• Practice Dilation Quiz

15
Dilation

• A transformation that changes the size of an
  object, but not the shape.
• A Dilation will be a similar figure, but not a
  congruent figure.
• Example

16
Dilate the object by a scale factor of ½
(2,2)
(-2,2)
(2,-2)
(-2,-2)
17
Dilate the object by a scale factor of 3
(-6,6)
(6,6)
(2,2)
(-2,2)
(2,-2)
(-2,-2)
(6,-6)
(-6,-6)