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The parallelogram D'E'F'G' is a dilation of the parallelogram DEFG. What is the scale factor of the dilation?


To determine the scale factor of the dilation between parallelogram \( D'E'F'G' \) and \( DEFG \), we need to compare corresponding side lengths of the two parallelograms.

From the given image:

- Side \( DE \) of the original parallelogram corresponds to side \( D'E' \) of the dilated parallelogram.  
- The length of \( DE \) is **2 units**, and the length of \( D'E' \) is **6 units**.  

### Formula for scale factor:
\[
\text{Scale Factor} = \frac{\text{Length of side in the dilated figure}}{\text{Length of side in the original figure}}
\]

Substitute the values:
\[
\text{Scale Factor} = \frac{6}{2} = 3
\]

### Final Answer:
The scale factor of the dilation is **3**.

Would you like a detailed explanation on dilation or how to calculate scale factors?  

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### Related Questions:
1. How do you find the scale factor if the areas of the figures are given?
2. What happens to the angles of a figure during a dilation?
3. How do you calculate a scale factor if the coordinates of vertices are provided?
4. How does a dilation affect the perimeter of a shape?
5. Can a dilation have a scale factor less than 1? What does it mean?

**Tip:** Always ensure that you compare corresponding sides or dimensions to calculate the scale factor correctly.

The parallelogram D'E'F'G' is a dilation of the parallelogram DEFG. What is the scale factor of the dilation?

Learn how to determine the scale factor of a dilation using parallelogram DEFG and its dilated image D'E'F'G'. Understand the formula and step-by-step solution to find the scale factor of 3, suitable for middle school geometry students.

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