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Dilations
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• Slide 1
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Dilations

December 4, 2020

• Question 2
300 seconds
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Q.

On Tuesday we were feeling pretty down and out about school and life. How are you doing today? Have things changed (for better or for worse?) at all for you?

Is there anything that I can do (other than not assigning any work) that would help make your world a little brighter?

*Remember: No one else will see these responses, they are just for you to talk to me*

• Question 3
60 seconds
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Q.

Warm-up: What does the scale factor do in a dilation?

Tells you how much the image grows or shrinks

Tells you what the center of dilation is

There's not enough information here to answer this

Nothing, it's unnecessary information

• Slide 4
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Scale Factors

What do they really do?

• Slide 5
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Scale Factors are just as they sound

• Factors (multipliers) that scale (change the size of) a shape

• Scale factors can do one of two things: grow or shrink an object

• A scale factor larger than one (>1) makes an object get larger --> could be a fraction or a whole number

• A scale factors smaller than one (<1) makes an object get smaller

• Question 6
120 seconds
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Q.

Which scale factors would increase an image?

$\frac{3}{2}$

$\frac{1}{2}$

$3.5$

$\frac{2}{1}$

5

• Question 7
120 seconds
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Q.

Which scale factors shrink an image?

$0.5$

$\frac{3}{4}$

$1$

$\frac{2}{1}$

$\frac{3}{2}$

• Question 8
120 seconds
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Q.

What are the properties of dilations?

Changes the size of an object

Changes the shape of an object

Changes one side but not the others

Changes all the sides equally

Changes angle measures

• Slide 9
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What happens if you aren't given the scale factor?

• Set up a proportion

• Solve for the missing side

• Slide 10
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But...what's a proportion?

A proportion is a ratio (fraction) that compares the corresponding pairs of sides

• Slide 11
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Proportion Example

The missing side, EF, can be found by setting up a proportion between the pairs of corresponding sides.
We know AB and DE are corresponding, and we know BC and EF are corresponding. So our proportion will be

$\frac{AB}{DE}\ =\ \frac{BC}{EF}$  which is  $\frac{5}{3}\ =\ \frac{2}{x}$

• Slide 12
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How do we solve a proportion now?

$\frac{5}{3}\ =\ \frac{2}{x}$

• Cross multiply (just like with regular fractions)   5x = 6

• Solve for x (divide both sides by 5)  $x\ =\ \frac{6}{5}\ =\ 1.2$

• Slide 13
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There is a proportions practice sheet in Google Classroom