https://file.aiquickdraw.com/mathbot/file/1726247167256n9q3kfxw.jpg

The problem is asking about dilation of a shape. Here’s how we can approach it:

### Problem Breakdown:
- **Original Shape**: The black shape.
- **New Shape**: The green shape, which is a dilation of the original.
  
### Types of Dilation:
- **Dilation** can be either an **enlargement** or a **reduction** based on the scale factor.
  - If the new shape is larger than the original, it's an **enlargement**.
  - If it's smaller, it's a **reduction**.

### Steps to Solve:
1. **Identify the change**: Compare the size of the green shape to the black shape. Based on visual observation, the green shape is smaller than the black one, meaning this is a **reduction**.

2. **Scale Factor Calculation**:
   - Pick a corresponding point on both shapes. For example, the vertical lines in the black shape go from \( y = 0 \) to \( y = 10 \), which gives a length of 10.
   - The green shape goes from \( y = 0 \) to \( y = 5 \), giving a length of 5.
   - The **scale factor** is the ratio of the new size to the original size, i.e., \( \frac{5}{10} = 0.5 \).

### Conclusion:
- This dilation is a **reduction** because the new shape is **smaller** than the original.
- The **scale factor** of this dilation is **0.5**.

Would you like more details or have any further questions? Here are five questions related to dilation:

1. What happens to the area of a shape when it undergoes dilation?
2. How do you determine the center of dilation?
3. What is the relationship between dilation and similarity in geometry?
4. Can dilation result in a shape that is flipped or rotated?
5. How would you calculate the scale factor if the dilation center is not the origin?

**Tip:** Always remember that the scale factor for dilation tells you how much each side of the shape is multiplied by to obtain the new shape.

The green shape is a dilation of the black shape (original). This dilation is an enlargement or reduction because the new shape is larger or smaller than the original. Find the scale factor of this dilation.

Understand how to calculate the scale factor of dilation for geometric shapes. In this problem, compare the green and black shapes to determine whether the dilation is an enlargement or reduction, and calculate the scale factor using simple geometry formulas.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation