To determine if Julia found the correct length of the run for the second triangle, we need to consider the properties of similar triangles.
The first triangle has a rise (vertical change) of 3 and a run (horizontal change) of 10. This creates a ratio of rise to run, or slope, of:
\[ \text{slope of first triangle} = \frac{\text{rise}}{\text{run}} = \frac{3}{10} \]
The second triangle has a rise of 7.5. Let \( r \) be the run of the second triangle. For the triangles to be similar, the ratios of their corresponding sides must be equal. Thus, we set up the proportion:
\[ \frac{3}{10} = \frac{7.5}{r} \]
To find \( r \), we can cross-multiply:
\[ 3r = 10 \times 7.5 \] \[ 3r = 75 \] \[ r = \frac{75}{3} = 25 \]
Therefore, for the second triangle to be similar to the first triangle, its run must equal 25.
Now, examining the options, Julia's approach appears to be in error if she didn't establish the correct proportion or if she incorrectly calculated the run. The most appropriate response is:
No, her proportion does not have the corresponding measures from corresponding figures in the same positions in the ratios.
This suggests that she may have set up the proportion incorrectly, leading to an incorrect answer for the run.
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