Question
Google Classroom
Microsoft Teams
Problem
is the image of
under a dilation whose center is
and scale factor is
.
Triangle ABC.
Which figure correctly shows
using the solid line?
Choose 1 answer:
Choose 1 answer:
(Choice A) Triangle A B C with a dilated triangle A prime B prime C prime to the inside of it. The scale factor between triangle A prime B prime C prime and triangle A B C is between zero and one half.
A
Triangle A B C with a dilated triangle A prime B prime C prime to the inside of it. The scale factor between triangle A prime B prime C prime and triangle A B C is between zero and one half.
(Choice B) Triangle A B C with a dilated triangle A prime B prime C prime to the inside of it. The scale factor between triangle A prime B prime C prime and triangle A B C is between one and one half.
B
Triangle A B C with a dilated triangle A prime B prime C prime to the inside of it. The scale factor between triangle A prime B prime C prime and triangle A B C is between one and one half.
(Choice C) Triangle A B C with a dilated triangle A prime B prime C prime to the inside of it. Segment A prime B prime is mapped on Segment A B. Segment A prime C prime is mapped on Segment A C. The scale factor between triangle A prime B prime C prime and triangle A B C is between zero and one half.
C
Triangle A B C with a dilated triangle A prime B prime C prime to the inside of it. Segment A prime B prime is mapped on Segment A B. Segment A prime C prime is mapped on Segment A C. The scale factor between triangle A prime B prime C prime and triangle A B C is between zero and one half.
(Choice D) Triangle A B C with a dilated triangle A prime B prime C prime to the inside of it. Segment A prime B prime is mapped on Segment A B. Segment A prime C prime is mapped on Segment A C. The scale factor between triangle A prime B prime C prime and triangle A B C is between one and one half.
D
Triangle A B C with a dilated triangle A prime B prime C prime to the inside of it. Segment A prime B prime is mapped on Segment A B. Segment A prime C prime is mapped on Segment A C. The scale factor between triangle A prime B prime C prime and triangle A B C is between one and one half.
Microsoft Teams
Problem
is the image of
under a dilation whose center is
and scale factor is
.
Triangle ABC.
Which figure correctly shows
using the solid line?
Choose 1 answer:
Choose 1 answer:
(Choice A) Triangle A B C with a dilated triangle A prime B prime C prime to the inside of it. The scale factor between triangle A prime B prime C prime and triangle A B C is between zero and one half.
A
Triangle A B C with a dilated triangle A prime B prime C prime to the inside of it. The scale factor between triangle A prime B prime C prime and triangle A B C is between zero and one half.
(Choice B) Triangle A B C with a dilated triangle A prime B prime C prime to the inside of it. The scale factor between triangle A prime B prime C prime and triangle A B C is between one and one half.
B
Triangle A B C with a dilated triangle A prime B prime C prime to the inside of it. The scale factor between triangle A prime B prime C prime and triangle A B C is between one and one half.
(Choice C) Triangle A B C with a dilated triangle A prime B prime C prime to the inside of it. Segment A prime B prime is mapped on Segment A B. Segment A prime C prime is mapped on Segment A C. The scale factor between triangle A prime B prime C prime and triangle A B C is between zero and one half.
C
Triangle A B C with a dilated triangle A prime B prime C prime to the inside of it. Segment A prime B prime is mapped on Segment A B. Segment A prime C prime is mapped on Segment A C. The scale factor between triangle A prime B prime C prime and triangle A B C is between zero and one half.
(Choice D) Triangle A B C with a dilated triangle A prime B prime C prime to the inside of it. Segment A prime B prime is mapped on Segment A B. Segment A prime C prime is mapped on Segment A C. The scale factor between triangle A prime B prime C prime and triangle A B C is between one and one half.
D
Triangle A B C with a dilated triangle A prime B prime C prime to the inside of it. Segment A prime B prime is mapped on Segment A B. Segment A prime C prime is mapped on Segment A C. The scale factor between triangle A prime B prime C prime and triangle A B C is between one and one half.
Answers
GPT-4o mini
To determine which figure shows the correct dilation of triangle ABC, we need to consider the following aspects:
1. **Dilation Center and Scale Factor**: A dilation transforms a figure by scaling it from a center point. If the scale factor is between 0 and 1, the figure will be reduced in size and placed inside the original figure. Conversely, if the scale factor is greater than 1, the figure will be enlarged and extend outside the original figure.
2. **Position of Dilation**: If the scale factor is between 0 and 1 (a contraction), the dilated triangle \( A'B'C' \) should be inside triangle \( ABC \). If the scale factor is greater than 1 (an expansion), triangle \( A'B'C' \) would be outside triangle \( ABC \).
Now let's analyze the options given:
- **Choice A**: This describes a dilation with a scale factor between 0 and 1, where triangle \( A'B'C' \) is inside triangle \( ABC \). This is consistent with a contraction.
- **Choice B**: This describes a dilation with a scale factor between 1 and ∞, leading to triangle \( A'B'C' \) residing outside triangle \( ABC \). This does not match with the condition of dilation being between 0 and 1.
- **Choice C**: This also indicates a scale factor between 0 and 1, with triangle \( A'B'C' \) inside \( ABC \) but mentions that segments are mapped to the original segments. This would suggest specific points corresponding to the original triangle, which may not apply universally depending on the center of dilation.
- **Choice D**: This suggests a dilation with a scale factor greater than 1, which is incorrect for a case where the resulting triangle should be inside the original triangle.
Given the context and the requirement for triangle \( A'B'C' \) to be correctly shown as dilated from triangle ABC with a scale factor less than 1, the best choice would be:
**Choice A**: Triangle ABC with a dilated triangle A'B'C' inside, with a scale factor between 0 and 1.
1. **Dilation Center and Scale Factor**: A dilation transforms a figure by scaling it from a center point. If the scale factor is between 0 and 1, the figure will be reduced in size and placed inside the original figure. Conversely, if the scale factor is greater than 1, the figure will be enlarged and extend outside the original figure.
2. **Position of Dilation**: If the scale factor is between 0 and 1 (a contraction), the dilated triangle \( A'B'C' \) should be inside triangle \( ABC \). If the scale factor is greater than 1 (an expansion), triangle \( A'B'C' \) would be outside triangle \( ABC \).
Now let's analyze the options given:
- **Choice A**: This describes a dilation with a scale factor between 0 and 1, where triangle \( A'B'C' \) is inside triangle \( ABC \). This is consistent with a contraction.
- **Choice B**: This describes a dilation with a scale factor between 1 and ∞, leading to triangle \( A'B'C' \) residing outside triangle \( ABC \). This does not match with the condition of dilation being between 0 and 1.
- **Choice C**: This also indicates a scale factor between 0 and 1, with triangle \( A'B'C' \) inside \( ABC \) but mentions that segments are mapped to the original segments. This would suggest specific points corresponding to the original triangle, which may not apply universally depending on the center of dilation.
- **Choice D**: This suggests a dilation with a scale factor greater than 1, which is incorrect for a case where the resulting triangle should be inside the original triangle.
Given the context and the requirement for triangle \( A'B'C' \) to be correctly shown as dilated from triangle ABC with a scale factor less than 1, the best choice would be:
**Choice A**: Triangle ABC with a dilated triangle A'B'C' inside, with a scale factor between 0 and 1.