The green shape is a dilation of the black shape.​​What is the scale factor of the dilation?​​

To find the scale factor of the dilation from the black shape to the green shape, we can follow these steps:

1. Break Down the Problem

1. Identify corresponding points on both shapes.
2. Measure the distance between these points in both shapes.

2. Relevant Concepts

• The scale factor $k$ of a dilation can be calculated using the formula: $k = \frac{\text{distance in green shape}}{\text{distance in black shape}}$

3. Analysis and Detail

1. Let’s denote the points as follows:

   • Choose a point $A$ on the black shape and its corresponding point $A'$ on the green shape.
   • Measure the distance $d_A$ between point $A$ to a specific point (e.g., the origin or another reference point) in the black shape.
   • Measure the distance $d_{A'}$ from point $A'$ to the same reference point in the green shape.

2. Calculate the scale factor using the measured distances: $k = \frac{d_{A'}}{d_{A}}$

4. Verify and Summarize

• Double check the calculated distances to ensure accuracy in the measurements.
• Summarize the findings with the calculated scale factor.

Final Answer

• Present the calculated scale factor $k$ based on the measurements provided.