https://file.aiquickdraw.com/mathbot/file/172703373410001cqe1os.jpg

Let's analyze the dilation described in the diagram.

We are given that pentagon **NQRTW** is dilated with the origin (0,0) as the center to create pentagon **N'Q'R'T'W'**. The location of vertex \( R' \) after the dilation is given as \( (6, 2) \).

### Steps:
1. **Initial Vertex of \( R \):**
   The vertex \( R \) in the original pentagon has coordinates \( (3, 1) \), as observed from the graph.

2. **Dilation Rule:**
   The dilation is centered at the origin. For a dilation, each point's distance from the origin is scaled by a factor. To find the dilation rule, we calculate the ratio between the coordinates of \( R' \) and \( R \).

   - \( R = (3, 1) \)
   - \( R' = (6, 2) \)

   Now, we can find the scale factor by comparing the coordinates of \( R \) and \( R' \):

   \[
   \text{Scale factor} = \frac{6}{3} = \frac{2}{1}
   \]

   The scale factor is **2**, which means that each coordinate of the original pentagon is multiplied by 2 to get the coordinates of the dilated pentagon.

### Conclusion:
The rule that best describes the dilation is **"Multiply both coordinates by 2."**

Would you like further clarification on this or additional details on how dilations work?

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Here are 5 related questions for further exploration:
1. What would be the new coordinates of point \( N' \) after applying the dilation?
2. How does the area of the dilated pentagon compare to the original pentagon?
3. What would happen if the scale factor were negative?
4. How do dilations affect angles and side lengths of polygons?
5. Can a dilation be considered a rigid transformation? Why or why not?

**Tip:** When determining a dilation, always look at the ratio of corresponding points' distances from the center of dilation.

Pentagon NQRTW was dilated with the origin as the center to create pentagon N'Q'R'T'W'. Vertex R' is located at (6,2). Which rule best describes the dilation?

Learn how to perform a dilation on a pentagon with the origin as the center. This problem demonstrates how to calculate the scale factor and apply it to the coordinates, focusing on vertex R' located at (6, 2). Suitable for students in Grades 8-10.

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