https://file.aiquickdraw.com/mathbot/file/1730998737730zuu6xqai.jpg

To solve the question of identifying the correct scale factor proportion for the enlargement shown, we need to analyze the dimensions given:

1. The smaller shape has dimensions \(1 \, \text{in.}\) by \(2 \, \text{in.}\).
2. The larger shape has dimensions \(x \, \text{in.}\) by \(6 \, \text{in.}\).

The goal is to find the proportion that represents the scale factor between the corresponding sides of the smaller and larger shapes.

### Step-by-Step Analysis

1. The ratio of the width of the smaller shape to the width of the larger shape is:
   \[
   \frac{1}{x}
   \]
   
2. The ratio of the length of the smaller shape to the length of the larger shape is:
   \[
   \frac{2}{6} = \frac{1}{3}
   \]

For the proportion to represent the scale factor, the two ratios must be equal. Therefore, the correct proportion is:
\[
\frac{1}{x} = \frac{2}{6}
\]

### Answer

The correct choice is the first option:
\[
\frac{1}{x} = \frac{2}{6}
\]

Would you like further clarification on this solution, or do you have any additional questions?

Here are some related questions for further practice:

1. How do you solve proportions when given different variables in each part?
2. What are some methods to simplify fractions in proportions?
3. How do you determine if two shapes are similar based on their proportions?
4. How would you solve for \( x \) in this proportion to find the missing dimension?
5. Can scale factors be used in three-dimensional shapes as well?

**Tip:** When working with proportions, ensure both sides of the equation compare corresponding dimensions to maintain accuracy.

Which is the scale factor proportion for the enlargement shown?

Learn how to find the scale factor proportion in similar figures by setting up and solving a proportion based on the dimensions of the shapes. This problem involves comparing ratios of corresponding sides in similar shapes, helping students understand basic concepts of enlargement and proportionality. Suitable for students in Grades 6-8.

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