Duplicate Question
The question on this page has been marked as a duplicate question.
Original Question
Julia was creating similar triangles in the coordinate plane. The first triangle had a rise of 3 and a run of 10. The second tr...Question
julia was creating similar triangles in the coordinate plane. The first triangle had a rise of 3 and a run of 10. The second triangle had a rise of 7.5.
Analyze Julia’s work to see if she found the correct length of the run for the second triangle to be similar to the first triangle.
Is Julia correct? If not, what was her mistake?
(1 point)
Responses
Yes, she is correct.
Yes, she is correct.
No, she needed to multiply 7.5 to both sides.
No, she needed to multiply 7.5 to both sides.
No, her proportion does not have the corresponding measures from corresponding figures in the same positions in the ratios.
No, her proportion does not have the corresponding measures from corresponding figures in the same positions in the ratios.
No, she needed to have the product of the numerators equal to the product of the denominators.
Analyze Julia’s work to see if she found the correct length of the run for the second triangle to be similar to the first triangle.
Is Julia correct? If not, what was her mistake?
(1 point)
Responses
Yes, she is correct.
Yes, she is correct.
No, she needed to multiply 7.5 to both sides.
No, she needed to multiply 7.5 to both sides.
No, her proportion does not have the corresponding measures from corresponding figures in the same positions in the ratios.
No, her proportion does not have the corresponding measures from corresponding figures in the same positions in the ratios.
No, she needed to have the product of the numerators equal to the product of the denominators.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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.
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.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.