Question
Elijah was trying to determine whether one triangle is a dilation of the other. Which statements about his solution are true? Check all that apply.
One triangle has side lengths of 3, 6, 7.5. Another triangle has side lengths of 5, 10, 12.5.
Elijah’s work:
3 is not a factor of 5, so it must be a relationship with addition.
3 + 2 = 5. 6 + 2 not-equals 10. 7.5 + 2 not-equals 12.5.
Therefore, the triangles are not proportional and cannot form a dilation.
Elijah did not know that scale factors can be fractions or decimals greater than zero.
Elijah did not know that dilations are proportional and the relationships are multiplicative, not additive.
Elijah should have compared the ratios Five-thirds = StartFraction 10 Over 6 EndFraction = StartFraction 12.5 Over 7.5 EndFraction to determine if they are equivalent.
Elijah needs to know which triangle is the pre-image and which triangle is the image in order to determine if they are proportional.
Elijah needs labels on the points to determine which sides correspond when writing the ratios.
One triangle has side lengths of 3, 6, 7.5. Another triangle has side lengths of 5, 10, 12.5.
Elijah’s work:
3 is not a factor of 5, so it must be a relationship with addition.
3 + 2 = 5. 6 + 2 not-equals 10. 7.5 + 2 not-equals 12.5.
Therefore, the triangles are not proportional and cannot form a dilation.
Elijah did not know that scale factors can be fractions or decimals greater than zero.
Elijah did not know that dilations are proportional and the relationships are multiplicative, not additive.
Elijah should have compared the ratios Five-thirds = StartFraction 10 Over 6 EndFraction = StartFraction 12.5 Over 7.5 EndFraction to determine if they are equivalent.
Elijah needs to know which triangle is the pre-image and which triangle is the image in order to determine if they are proportional.
Elijah needs labels on the points to determine which sides correspond when writing the ratios.
Answers
GPT-4o mini
Based on the provided statements regarding Elijah's solution to determine if one triangle is a dilation of the other, the following statements are true:
1. **Elijah did not know that scale factors can be fractions or decimals greater than zero.** - True. He incorrectly assumed only whole number factors are possible.
2. **Elijah did not know that dilations are proportional and the relationships are multiplicative, not additive.** - True. His method involved addition instead of using multiplicative ratios.
3. **Elijah should have compared the ratios \( \frac{5}{3} = \frac{10}{6} = \frac{12.5}{7.5} \) to determine if they are equivalent.** - True. This is the proper way to verify if the triangles are dilations of each other by checking if the ratios of corresponding sides are equal.
4. **Elijah needs to know which triangle is the pre-image and which triangle is the image in order to determine if they are proportional.** - True. Understanding which triangle is which is crucial for determining proportionality.
5. **Elijah needs labels on the points to determine which sides correspond when writing the ratios.** - True. To establish a clear correspondence between sides, labeling the vertices of the triangles is important.
Overall, all the statements you've listed are true regarding Elijah's process to determine if the triangles are dilations of each other.
1. **Elijah did not know that scale factors can be fractions or decimals greater than zero.** - True. He incorrectly assumed only whole number factors are possible.
2. **Elijah did not know that dilations are proportional and the relationships are multiplicative, not additive.** - True. His method involved addition instead of using multiplicative ratios.
3. **Elijah should have compared the ratios \( \frac{5}{3} = \frac{10}{6} = \frac{12.5}{7.5} \) to determine if they are equivalent.** - True. This is the proper way to verify if the triangles are dilations of each other by checking if the ratios of corresponding sides are equal.
4. **Elijah needs to know which triangle is the pre-image and which triangle is the image in order to determine if they are proportional.** - True. Understanding which triangle is which is crucial for determining proportionality.
5. **Elijah needs labels on the points to determine which sides correspond when writing the ratios.** - True. To establish a clear correspondence between sides, labeling the vertices of the triangles is important.
Overall, all the statements you've listed are true regarding Elijah's process to determine if the triangles are dilations of each other.