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5. The larger figure is a dilation of the original figure. Which two statements below are true?

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Captionless Image
The dilation is an enlargement.
The dilation is a reduction.
The dilation has a scale factor of 1/2.
The dilation has a scale factor of 2.
The dilation has a scale factor of 1/4.

1 answer

To determine which two statements are true about the dilation, we need to analyze the relationship between the original figure and the larger figure:

1. **The dilation is an enlargement.**
- If the original figure has been made larger, this statement would be true.

2. **The dilation is a reduction.**
- If the original figure has been made smaller, this statement would be true.

3. **The dilation has a scale factor of 1/2.**
- A scale factor of 1/2 would mean the new figure is half the size of the original, indicating a reduction.

4. **The dilation has a scale factor of 2.**
- A scale factor of 2 would mean the new figure is twice the size of the original, indicating an enlargement.

5. **The dilation has a scale factor of 1/4.**
- A scale factor of 1/4 would mean the new figure is one-fourth the size of the original, indicating a significant reduction.

Without the image, I can provide a general method to decide which statements are true:

- If the larger figure is an **enlargement** of the original, then the dilation is an enlargement, and the scale factor is greater than 1. It can be either 2, 3, etc.

- If the larger figure is a **reduction** of the original, then the dilation is a reduction, and the scale factor is between 0 and 1 (such as 1/2 or 1/4).

Let's choose statements assuming the figure is an enlargement (a larger figure than the original):

1. The dilation is an enlargement.
2. The dilation has a scale factor greater than 1 (e.g., the dilation has a scale factor of 2).

Thus, the two true statements would likely be:
1. The dilation is an enlargement.
2. The dilation has a scale factor of 2.

However, for precise verification, one needs to measure or visualize the comparative sizes of the original and the dilated figure.