Question
A triangle with vertices at (1,1), (4,1), and (1,3) is transformed to a triangle with vertices at (3,1), (6,1), and (3,3). Which transformation was applied?
Answers
Answer
A triangle with vertices at (2,3), (3,5), and (5,3) is transformed to a triangle with vertices at (4,6), (5,8), and (7,6). Which transformation was applied?
*
1 point
Translation 2 units up and 2 units right
Translation 2 units up and 2 units left
Rotation 180 degrees about the origin
Rotation 90 degrees clockwise about the origin
*
1 point
Translation 2 units up and 2 units right
Translation 2 units up and 2 units left
Rotation 180 degrees about the origin
Rotation 90 degrees clockwise about the origin
Answer
A square with vertices at (3,3), (6,3), (6,6), and (3,6) is transformed to a square with vertices at (−3,−3), (−6,−3), (−6,−6), and (−3,−6). Which transformation was applied?
*
1 point
Translation 6 units left and 6 units down
Translation 6 units right and 6 units up
Rotation 180 degrees about the origin
Rotation 90 degrees clockwise about the origin
*
1 point
Translation 6 units left and 6 units down
Translation 6 units right and 6 units up
Rotation 180 degrees about the origin
Rotation 90 degrees clockwise about the origin
Answer
A pentagon with vertices at (1,1), (2,3), (4,3), (5,1), and (3,0) is transformed to a pentagon with vertices at (1,−1), (2,−3), (4,−3), (5,−1), and (3,0). Which transformation was applied?
*
1 point
Rotation 180 degrees about the origin
Rotation 90 degrees counterclockwise about the origin
Translation 2 units down
Reflection over the x-axis
*
1 point
Rotation 180 degrees about the origin
Rotation 90 degrees counterclockwise about the origin
Translation 2 units down
Reflection over the x-axis
Answer
A rectangle with vertices at (2,3), (5,3), (5,6), and (2,6) is transformed to a rectangle with vertices at (2,−3), (5,−3), (5,−6), and (2,−6). Which transformation was applied?
*
1 point
Reflection over the x-axis
Reflection over the y-axis
Rotation 180 degrees about the origin
Translation 6 units down
*
1 point
Reflection over the x-axis
Reflection over the y-axis
Rotation 180 degrees about the origin
Translation 6 units down
Answered by
GPT-4o mini
To determine the transformation applied to the triangle with vertices at (1,1), (4,1), and (1,3) to obtain the triangle with vertices at (3,1), (6,1), and (3,3), we can analyze the coordinates of the vertices before and after the transformation.
1. **Original Vertices:**
- A: (1,1)
- B: (4,1)
- C: (1,3)
2. **Transformed Vertices:**
- A': (3,1)
- B': (6,1)
- C': (3,3)
Now, let's observe the changes made to each vertex:
- Vertex A (1,1) transformed to A' (3,1):
- The x-coordinate changed from 1 to 3 (+2).
- The y-coordinate remained the same.
- Vertex B (4,1) transformed to B' (6,1):
- The x-coordinate changed from 4 to 6 (+2).
- The y-coordinate remained the same.
- Vertex C (1,3) transformed to C' (3,3):
- The x-coordinate changed from 1 to 3 (+2).
- The y-coordinate remained the same.
From this analysis, we see that the transformation for all vertices involved:
- An increase of 2 in the x-coordinate.
- No change in the y-coordinate.
Thus, the transformation applies a translation (or shift) of 2 units to the right along the x-axis.
In conclusion, the transformation that was applied is a **translation of (2, 0)**.
1. **Original Vertices:**
- A: (1,1)
- B: (4,1)
- C: (1,3)
2. **Transformed Vertices:**
- A': (3,1)
- B': (6,1)
- C': (3,3)
Now, let's observe the changes made to each vertex:
- Vertex A (1,1) transformed to A' (3,1):
- The x-coordinate changed from 1 to 3 (+2).
- The y-coordinate remained the same.
- Vertex B (4,1) transformed to B' (6,1):
- The x-coordinate changed from 4 to 6 (+2).
- The y-coordinate remained the same.
- Vertex C (1,3) transformed to C' (3,3):
- The x-coordinate changed from 1 to 3 (+2).
- The y-coordinate remained the same.
From this analysis, we see that the transformation for all vertices involved:
- An increase of 2 in the x-coordinate.
- No change in the y-coordinate.
Thus, the transformation applies a translation (or shift) of 2 units to the right along the x-axis.
In conclusion, the transformation that was applied is a **translation of (2, 0)**.
Answered by
GPT-4o mini
To determine the transformation applied to the triangle with vertices at (2,3), (3,5), and (5,3) to obtain the triangle with vertices at (4,6), (5,8), and (7,6), we can analyze the coordinates of the vertices before and after the transformation.
1. **Original Vertices:**
- A: (2,3)
- B: (3,5)
- C: (5,3)
2. **Transformed Vertices:**
- A': (4,6)
- B': (5,8)
- C': (7,6)
Now, we can find the changes in the coordinates for each vertex:
- Vertex A (2,3) transformed to A' (4,6):
- The x-coordinate changed from 2 to 4 (+2).
- The y-coordinate changed from 3 to 6 (+3).
- Vertex B (3,5) transformed to B' (5,8):
- The x-coordinate changed from 3 to 5 (+2).
- The y-coordinate changed from 5 to 8 (+3).
- Vertex C (5,3) transformed to C' (7,6):
- The x-coordinate changed from 5 to 7 (+2).
- The y-coordinate changed from 3 to 6 (+3).
From this analysis, we see that the transformation for all vertices involved:
- An increase of 2 in the x-coordinate.
- An increase of 3 in the y-coordinate.
Thus, the transformation can be described as a translation of (2, 3).
Among the options provided, the correct transformation that matches increases of 2 units right and 3 units up is not explicitly listed. However, based on the options, **the closest interpretation might align with "Translation 2 units up and 2 units right,"** but be aware that it accurately translates 2 units right and 3 units up instead.
If the question strictly adheres to the provided options without a perfect match, the answer would rely on the interpretation of the context.
1. **Original Vertices:**
- A: (2,3)
- B: (3,5)
- C: (5,3)
2. **Transformed Vertices:**
- A': (4,6)
- B': (5,8)
- C': (7,6)
Now, we can find the changes in the coordinates for each vertex:
- Vertex A (2,3) transformed to A' (4,6):
- The x-coordinate changed from 2 to 4 (+2).
- The y-coordinate changed from 3 to 6 (+3).
- Vertex B (3,5) transformed to B' (5,8):
- The x-coordinate changed from 3 to 5 (+2).
- The y-coordinate changed from 5 to 8 (+3).
- Vertex C (5,3) transformed to C' (7,6):
- The x-coordinate changed from 5 to 7 (+2).
- The y-coordinate changed from 3 to 6 (+3).
From this analysis, we see that the transformation for all vertices involved:
- An increase of 2 in the x-coordinate.
- An increase of 3 in the y-coordinate.
Thus, the transformation can be described as a translation of (2, 3).
Among the options provided, the correct transformation that matches increases of 2 units right and 3 units up is not explicitly listed. However, based on the options, **the closest interpretation might align with "Translation 2 units up and 2 units right,"** but be aware that it accurately translates 2 units right and 3 units up instead.
If the question strictly adheres to the provided options without a perfect match, the answer would rely on the interpretation of the context.
Answered by
GPT-4o mini
To determine the transformation applied to the square with vertices at (3,3), (6,3), (6,6), and (3,6) to obtain the square with vertices at (−3,−3), (−6,−3), (−6,−6), and (−3,−6), we can analyze the changes in the coordinates of the vertices.
1. **Original Vertices:**
- A: (3,3)
- B: (6,3)
- C: (6,6)
- D: (3,6)
2. **Transformed Vertices:**
- A': (−3,−3)
- B': (−6,−3)
- C': (−6,−6)
- D': (−3,−6)
Now, let's examine how each vertex has changed:
- Vertex A (3,3) transformed to A' (−3,−3):
- The x-coordinate changed from 3 to −3 (decreased by 6).
- The y-coordinate changed from 3 to −3 (decreased by 6).
- Vertex B (6,3) transformed to B' (−6,−3):
- The x-coordinate changed from 6 to −6 (decreased by 12).
- The y-coordinate remained the same (3 to -3).
- Vertex C (6,6) transformed to C' (−6,−6):
- The x-coordinate changed from 6 to −6 (decreased by 12).
- The y-coordinate changed from 6 to −6 (decreased by 12).
- Vertex D (3,6) transformed to D' (−3,−6):
- The x-coordinate changed from 3 to −3 (decreased by 6).
- The y-coordinate changed from 6 to −6 (decreased by 12).
From this analysis, we see that there is a consistent pattern of transformation:
The pattern indicates that it’s not just a translation (as the translations would not yield this specific change in coordinates).
The key transformation can be identified as a **rotation of 180 degrees about the origin**. All vertices have effectively undergone this transformation, which results in their coordinates being negated:
- (x, y) becomes (-x, -y).
Therefore, the correct answer is **Rotation 180 degrees about the origin**.
1. **Original Vertices:**
- A: (3,3)
- B: (6,3)
- C: (6,6)
- D: (3,6)
2. **Transformed Vertices:**
- A': (−3,−3)
- B': (−6,−3)
- C': (−6,−6)
- D': (−3,−6)
Now, let's examine how each vertex has changed:
- Vertex A (3,3) transformed to A' (−3,−3):
- The x-coordinate changed from 3 to −3 (decreased by 6).
- The y-coordinate changed from 3 to −3 (decreased by 6).
- Vertex B (6,3) transformed to B' (−6,−3):
- The x-coordinate changed from 6 to −6 (decreased by 12).
- The y-coordinate remained the same (3 to -3).
- Vertex C (6,6) transformed to C' (−6,−6):
- The x-coordinate changed from 6 to −6 (decreased by 12).
- The y-coordinate changed from 6 to −6 (decreased by 12).
- Vertex D (3,6) transformed to D' (−3,−6):
- The x-coordinate changed from 3 to −3 (decreased by 6).
- The y-coordinate changed from 6 to −6 (decreased by 12).
From this analysis, we see that there is a consistent pattern of transformation:
The pattern indicates that it’s not just a translation (as the translations would not yield this specific change in coordinates).
The key transformation can be identified as a **rotation of 180 degrees about the origin**. All vertices have effectively undergone this transformation, which results in their coordinates being negated:
- (x, y) becomes (-x, -y).
Therefore, the correct answer is **Rotation 180 degrees about the origin**.
Answered by
GPT-4o mini
To determine the transformation applied to the pentagon with vertices at (1,1), (2,3), (4,3), (5,1), and (3,0) to obtain the pentagon with vertices at (1,−1), (2,−3), (4,−3), (5,−1), and (3,0), we can analyze the changes in the coordinates of the vertices.
1. **Original Vertices:**
- A: (1,1)
- B: (2,3)
- C: (4,3)
- D: (5,1)
- E: (3,0)
2. **Transformed Vertices:**
- A': (1,−1)
- B': (2,−3)
- C': (4,−3)
- D': (5,−1)
- E': (3,0)
Now, let's examine how each vertex has changed:
- Vertex A (1,1) transformed to A' (1,−1):
- The x-coordinate remained the same.
- The y-coordinate changed from 1 to −1 (it is reflected across the x-axis).
- Vertex B (2,3) transformed to B' (2,−3):
- The x-coordinate remained the same.
- The y-coordinate changed from 3 to −3 (it is reflected across the x-axis).
- Vertex C (4,3) transformed to C' (4,−3):
- The x-coordinate remained the same.
- The y-coordinate changed from 3 to −3 (it is reflected across the x-axis).
- Vertex D (5,1) transformed to D' (5,−1):
- The x-coordinate remained the same.
- The y-coordinate changed from 1 to −1 (it is reflected across the x-axis).
- Vertex E (3,0) transformed to E' (3,0):
- Both the x and y coordinates remained the same (this point lies on the x-axis and is unchanged).
Based on this analysis, we can conclude that the transformation applied is **reflection over the x-axis**.
Therefore, the correct answer is **Reflection over the x-axis**.
1. **Original Vertices:**
- A: (1,1)
- B: (2,3)
- C: (4,3)
- D: (5,1)
- E: (3,0)
2. **Transformed Vertices:**
- A': (1,−1)
- B': (2,−3)
- C': (4,−3)
- D': (5,−1)
- E': (3,0)
Now, let's examine how each vertex has changed:
- Vertex A (1,1) transformed to A' (1,−1):
- The x-coordinate remained the same.
- The y-coordinate changed from 1 to −1 (it is reflected across the x-axis).
- Vertex B (2,3) transformed to B' (2,−3):
- The x-coordinate remained the same.
- The y-coordinate changed from 3 to −3 (it is reflected across the x-axis).
- Vertex C (4,3) transformed to C' (4,−3):
- The x-coordinate remained the same.
- The y-coordinate changed from 3 to −3 (it is reflected across the x-axis).
- Vertex D (5,1) transformed to D' (5,−1):
- The x-coordinate remained the same.
- The y-coordinate changed from 1 to −1 (it is reflected across the x-axis).
- Vertex E (3,0) transformed to E' (3,0):
- Both the x and y coordinates remained the same (this point lies on the x-axis and is unchanged).
Based on this analysis, we can conclude that the transformation applied is **reflection over the x-axis**.
Therefore, the correct answer is **Reflection over the x-axis**.
Answered by
GPT-4o mini
To determine the transformation applied to the rectangle with vertices at (2,3), (5,3), (5,6), and (2,6) that resulted in the rectangle with vertices at (2,−3), (5,−3), (5,−6), and (2,−6), we can analyze the changes in the coordinates of the vertices.
1. **Original Vertices:**
- A: (2,3)
- B: (5,3)
- C: (5,6)
- D: (2,6)
2. **Transformed Vertices:**
- A': (2,−3)
- B': (5,−3)
- C': (5,−6)
- D': (2,−6)
Now, let's examine how each vertex has changed:
- Vertex A (2,3) transformed to A' (2,−3):
- The x-coordinate remained the same.
- The y-coordinate changed from 3 to −3 (a reflection across the x-axis).
- Vertex B (5,3) transformed to B' (5,−3):
- The x-coordinate remained the same.
- The y-coordinate changed from 3 to −3 (a reflection across the x-axis).
- Vertex C (5,6) transformed to C' (5,−6):
- The x-coordinate remained the same.
- The y-coordinate changed from 6 to −6 (a reflection across the x-axis).
- Vertex D (2,6) transformed to D' (2,−6):
- The x-coordinate remained the same.
- The y-coordinate changed from 6 to −6 (a reflection across the x-axis).
From this analysis, we conclude that all vertices have undergone a change where the y-coordinates have been negated while the x-coordinates have remained the same. This is characteristic of a reflection over the x-axis.
Therefore, the correct answer is **Reflection over the x-axis**.
1. **Original Vertices:**
- A: (2,3)
- B: (5,3)
- C: (5,6)
- D: (2,6)
2. **Transformed Vertices:**
- A': (2,−3)
- B': (5,−3)
- C': (5,−6)
- D': (2,−6)
Now, let's examine how each vertex has changed:
- Vertex A (2,3) transformed to A' (2,−3):
- The x-coordinate remained the same.
- The y-coordinate changed from 3 to −3 (a reflection across the x-axis).
- Vertex B (5,3) transformed to B' (5,−3):
- The x-coordinate remained the same.
- The y-coordinate changed from 3 to −3 (a reflection across the x-axis).
- Vertex C (5,6) transformed to C' (5,−6):
- The x-coordinate remained the same.
- The y-coordinate changed from 6 to −6 (a reflection across the x-axis).
- Vertex D (2,6) transformed to D' (2,−6):
- The x-coordinate remained the same.
- The y-coordinate changed from 6 to −6 (a reflection across the x-axis).
From this analysis, we conclude that all vertices have undergone a change where the y-coordinates have been negated while the x-coordinates have remained the same. This is characteristic of a reflection over the x-axis.
Therefore, the correct answer is **Reflection over the x-axis**.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.