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To determine the scale factor of the dilation between Figure A and Figure B, we need to compare corresponding dimensions of both figures (since the dilation is centered at the origin).

Let's break it down:

1. **Measure the dimensions of Figure A**:  
   - The height of Figure A is from approximately \( y = 14 \) to \( y = 18 \), which gives a height of 4 units.
   - The width of Figure A is from approximately \( x = 16 \) to \( x = 20 \), which gives a width of 4 units.

2. **Measure the dimensions of Figure B**:  
   - The height of Figure B is from \( y = 6 \) to \( y = 8 \), giving a height of 2 units.
   - The width of Figure B is from \( x = 6 \) to \( x = 8 \), giving a width of 2 units.

3. **Calculate the scale factor**:  
   - The scale factor \( k \) is the ratio of the dimensions of Figure B to Figure A. We can use either the width or the height:
     \[
     k = \frac{\text{Height of Figure B}}{\text{Height of Figure A}} = \frac{2}{4} = \frac{1}{2}
     \]
     or
     \[
     k = \frac{\text{Width of Figure B}}{\text{Width of Figure A}} = \frac{2}{4} = \frac{1}{2}
     \]

Therefore, the scale factor of the dilation is \( \frac{1}{2} \).

Would you like more details or have any further questions?

Here are some related questions you might want to consider:
1. How does the scale factor affect the area of the dilated figure?
2. What happens to the coordinates of a point when dilated by a factor of \( \frac{1}{2} \) about the origin?
3. Can a dilation ever result in a larger figure than the original? If so, what would the scale factor be?
4. How would the scale factor change if the dilation made Figure B twice as large as Figure A?
5. How can you determine the center of dilation if it's not given?

**Tip**: In a dilation, all corresponding sides of the figure are proportional to the scale factor, and the angle measures remain unchanged.

A dilation centered at the origin is applied to Figure A. The result is Figure B. What is the scale factor of the dilation?

Learn how to find the scale factor of a dilation centered at the origin. In this example, Figure A is transformed into Figure B. Explore geometric concepts like dilation, scaling, and transformations, suitable for students in Grades 8-10.

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