https://file.aiquickdraw.com/mathbot/file/1727019102469wadvbdz0.jpg

The problem in the image asks to determine whether the dilation from Figure A to Figure B is an enlargement or a reduction and to find the scale factor. It also requires solving for the variables \(x\), \(y\), and \(z\).

### Part (a):
- **Figure A** dimensions: \(6 \times 3\)
- **Figure B** dimensions: \(2 \times z\)
  
  To find the scale factor, divide the dimensions of Figure B by Figure A:
  
  \[
  \text{Scale factor} = \frac{\text{Dimensions of B}}{\text{Dimensions of A}} = \frac{2}{6} = \frac{1}{3}
  \]

  This represents a **reduction** since the scale factor is less than 1. 

  Now, let's find \(z\) using the scale factor:
  
  \[
  \frac{z}{3} = \frac{1}{3}
  \]
  Solving for \(z\), we get \(z = 1\).

  So, for part (a), the scale factor is \( \frac{1}{3} \), and \(z = 1\).

---

### Part (b):
- **Figure A** dimensions: \(2 \times y\)
- **Figure B** dimensions: \(7.5 \times 5\)

  Again, to find the scale factor, divide the dimensions of Figure B by Figure A:
  
  \[
  \text{Scale factor} = \frac{7.5}{2} = 3.75
  \]

  This represents an **enlargement** since the scale factor is greater than 1.

  Now, let's find \(y\) using the scale factor:
  
  \[
  \frac{y}{5} = 3.75
  \]
  Solving for \(y\), we get \(y = 18.75\).

  So, for part (b), the scale factor is \(3.75\), and \(y = 18.75\).

---

Would you like more detailed steps on any part? Here are 5 related questions:

1. What is the formula for finding the scale factor between two figures?
2. How do you determine if a dilation is an enlargement or a reduction?
3. What happens to the perimeter of a figure when it is dilated?
4. How does the scale factor affect the area of a dilated figure?
5. Can the scale factor ever be negative in a geometric dilation?

**Tip**: Always compare corresponding sides when finding the scale factor.

Determine whether the dilation from Figure A to Figure B is an enlargement or a reduction. Then, find the values of the variables.

This problem involves determining whether the dilation between two figures represents an enlargement or reduction. Learn how to calculate the scale factor and solve for variables using geometric transformations and proportional reasoning.

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