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## 8th grade (Illustrative Mathematics)

### Unit 2: Lesson 3

Lesson 7: Similar polygons

# Dilations: scale factor

Find the scale factor of a dilation that maps a given figure to another one.

## Want to join the conversation?

• How do you find the scale factor without the origin at zero?
• Dont need to, as for example two and example three, they didnt give any origin so Khan said that we dont even need to draw it since they didnt give enough information; that is the origin.

The video explains how to find the scale factor of a dilation, and how to find the afterimage of a figure that went into a dilation (without the figure being drawn), and how to find the pre-image of a figure that went into a dilation (without the figure being drawn).

Hope this made sense.
• whats the opposite of a dilation
• A dilation can be an image larger or smaller than the first.
• At , why can't the scale factor be 3, not 1/3? Is there a specific rule where it is either a smaller scale or larger? Thanks so much for the help!
• Figures are defined by pre-image and image, so the image would be the dilation while the pre-image is the original figure. So with the preimage being larger, the dilation has to be a fraction less than 1. IF you considered the small pentagon to be the preimage which would be a different question, then the image gets bigger and the scale factor would be 3.
• At how do I know what to find the scale factor of? If it's big shape to small shape or small shape to big shape?
• Great question!
The shape that is labeled prime (with an apostrophe `'` near each letter) is the image (changed form) of the original shape. Therefore, if the big shape is labeled, say, `A'B'C'D'`, you'll know that the dilation transformed the small shape to the big shape, and vice-versa.
Get it? Got it? Good.
- littlemissdeena
• any other easy way to slove it?
• Just find the difference between the segments and its just simple division or multiplication after that.
• Why did you have to multiply by 1/3
• He is measuring how much the factor increased so for example 1/3 being divided by 3
• How come in the 3rd example he multiplies 2 by 5/2. but it the last example he divides by 2??
• There are two different questions,
first starts with the pre-image (non-prime figure) in the diagram, and asks about the image (prime figure)
second starts with the image (prime figure) and asks to go backwards to the pre-image (non-prime), going backwards requires to do opposite of multiply by 2
• How do you make this more easy?
• To simplify this process, you can easily multiply the scale factor with the original sides to create the prime sides. Does this help?