1. **State the problem:** We are given two triangles, \(\triangle ABC\) and its dilation \(\triangle A'B'C'\), and we want to find the correct scale factor relating the two triangles. 2. **Recall the scale factor definition:** The scale factor of a dilation is the ratio of a side length in the image triangle to the corresponding side length in the original triangle. 3. **Given information:** The user states the correct scale factor is \(\frac{5}{7}\). 4. **Analyze the options:** - A. "Your friend found the ratio between non-corresponding sides." This would not give the correct scale factor. - B. "Your friend found the ratio between two sides of the image triangle." This is a ratio within the image triangle only, not between image and original. - C. "Your friend found the scale factor that enlarges \(\triangle A'B'C'\) to \(\triangle ABC\)." This means the ratio from image to original, which is the reciprocal of the scale factor from original to image. - D. "Your friend found the ratio between two sides of the original triangle." This is a ratio within the original triangle only. 5. **Conclusion:** Since the correct scale factor is \(\frac{5}{7}\), which is less than 1, it means the image is smaller than the original. If your friend found \(\frac{7}{5}\), that would be the scale factor enlarging \(\triangle A'B'C'\) back to \(\triangle ABC\), matching option C. **Final answer:** C. Your friend found the scale factor that enlarges \(\triangle A'B'C'\) to \(\triangle ABC\).