Dilations

Dilations

December 4, 2020

Open Ended

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*

Multiple Choice

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

Scale Factors

What do they really do?

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

Multiple Select

Which scale factors would increase an image?

• $\frac{3}{2}$

• $\frac{1}{2}$

• $3.5$

• $\frac{2}{1}$

• 5
  

Multiple Select

Which scale factors shrink an image?

• $0.5$

• $\frac{3}{4}$

• $1$

• $\frac{2}{1}$

• $\frac{3}{2}$

Multiple Select

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

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

• Set up a proportion

• Solve for the missing side

But...what's a proportion?

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

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  $\frac{5}{3}\ =\ \frac{2}{x}$  

How do we solve a proportion now?

• Set up your proportion

   $\frac{5}{3}\ =\ \frac{2}{x}$  

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

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

There is a proportions practice sheet in Google Classroom

Please go work on that

Email me if you have any questions :)