https://file.aiquickdraw.com/mathbot/file/17268340348885htkgx8f.jpg

To find the scale factor that maps Figure 2 to Figure 1, we need to compare corresponding sides of the two triangles.

### Steps to determine the scale factor:

1. Identify corresponding points between the two figures. Let's assume:
   - \( A \leftrightarrow Q \)
   - \( C \leftrightarrow S \)
   - The third vertex of the smaller triangle corresponds to the third vertex of the larger triangle.

2. Measure the length of corresponding sides using the grid provided. Since both figures are on the same grid, you can count the number of grid units between the points.

3. The scale factor is found by taking the ratio of the lengths of a side in Figure 1 to the corresponding side in Figure 2.

### Let's analyze the triangles:
- In Figure 1 (smaller triangle), count the units for side \( AC \).
- In Figure 2 (larger triangle), count the units for side \( QS \).

Now, divide the length of side \( AC \) by the length of side \( QS \).

Let me measure the units from the image:

- Length of \( AC \) (Figure 1) = 3 grid units.
- Length of \( QS \) (Figure 2) = 6 grid units.

### Scale Factor Calculation:
The scale factor from Figure 2 to Figure 1 is:

\[
\text{Scale Factor} = \frac{\text{Length of side in Figure 1}}{\text{Length of corresponding side in Figure 2}} = \frac{3}{6} = \frac{1}{2}
\]

Thus, the scale factor that maps Figure 2 to Figure 1 is **\( \frac{1}{2} \)**.

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Would you like more details or have any questions?

Here are five related questions to expand your understanding:

1. How do you determine corresponding points in similar triangles?
2. What happens if the scale factor is greater than 1?
3. Can the scale factor be a negative number in certain cases?
4. How does changing the scale factor affect the area of the figure?
5. What are some real-world applications of using scale factors in geometry?

**Tip:** When calculating scale factors, always ensure the corresponding points or sides are correctly identified, as this is key to an accurate calculation.

WHAT SCALE FACTOR MAPS FIGURE 2 TO FIGURE 1?

Learn how to find the scale factor that maps Figure 2 to Figure 1 in this geometry problem. The solution involves comparing the lengths of corresponding sides of two similar triangles and applying the formula for the scale factor. Suitable for Grades 6-8.

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