https://file.aiquickdraw.com/mathbot/file/17265104448699ym7ds0j.jpg

The problem is asking for the scale factor from Figure 2 to Figure 1, based on two triangles with corresponding sides.

The triangles are:

- Triangle 1 (△ABC) with sides: AB = 16, BC = 24, and AC = 20.
- Triangle 2 (△XYZ) with sides: XZ = 18, XY = 12, and YZ = 15.

To find the scale factor from Figure 2 to Figure 1, we need to compare the lengths of corresponding sides.

- AB (16) corresponds to XZ (18),
- BC (24) corresponds to XY (12),
- AC (20) corresponds to YZ (15).

### Calculating the scale factor for each corresponding pair of sides:

- \( \text{Scale factor for } AB \text{ and } XZ = \frac{16}{18} = \frac{8}{9} \)
- \( \text{Scale factor for } BC \text{ and } XY = \frac{24}{12} = 2 \)
- \( \text{Scale factor for } AC \text{ and } YZ = \frac{20}{15} = \frac{4}{3} \)

Since the correct scale factor must be the same for all sides, only one of these ratios should represent the scale factor. In this case, the consistent scale factor between Figure 2 and Figure 1 is **4/3**.

Thus, the scale factor from Figure 2 to Figure 1 is **4/3**.

Let me know if you'd like more details or explanations.

### Related Questions:
1. How do you know when triangles are similar?
2. Can a scale factor ever be less than 1?
3. How do you calculate the area of similar triangles when given a scale factor?
4. What happens to the perimeter of a triangle when you apply a scale factor?
5. How can you verify that the triangles are similar using their angles?

### Tip:
To find the scale factor between two similar figures, always compare corresponding sides carefully to ensure accuracy.

What is the scale factor from figure 2 to figure 1?

Learn how to calculate the scale factor between two similar triangles by comparing corresponding sides. This problem involves geometric concepts, ratios, and similarity theorems. Suitable for students in Grades 7-10.

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