Question
Draw a figure with 3-5 sides. Label each vertex. Perform a composition transformation on your pre-image. Be sure to make note of vertex coordinates at each step. In discussion give the coordinates of your pre-image and image. (You may include a picture of the pre-image & image). You may also post your transformation rules, but one rule must be incorrect.
After you have posted your coordinates and rules, respond to two of your classmates' posts. In your response to each post:
Write the correct transformation rules for the image coordinates given by a classmate.
Find the correct coordinates for the transformation rules your classmate gave.
After you have posted your coordinates and rules, respond to two of your classmates' posts. In your response to each post:
Write the correct transformation rules for the image coordinates given by a classmate.
Find the correct coordinates for the transformation rules your classmate gave.
Answers
Answer
can u make it shortter please
Answer
like this for example
(2,6), (4,3), and (8,9)
Translation: Go two units ahead and six points to the left.
In a 270-clockwise rotation
Dilation: Inaccurate scale factor of 0.8
(2,6), (4,3), and (8,9)
Translation: Go two units ahead and six points to the left.
In a 270-clockwise rotation
Dilation: Inaccurate scale factor of 0.8
Answer
can u do it like this
ex Translation: (8,8) (1,6) (4,) (incorrect)
Reflection: 180 clockwise
Dilation: Scale factor 3
ex Translation: (8,8) (1,6) (4,) (incorrect)
Reflection: 180 clockwise
Dilation: Scale factor 3
Answered by
GPT-4o mini
### Pre-Image:
Let's create a triangle as our pre-image with the following vertices:
- A(1, 1)
- B(4, 1)
- C(2.5, 3)
The coordinates of the pre-image triangle ABC are:
- A: (1, 1)
- B: (4, 1)
- C: (2.5, 3)
### Transformation Rules:
1. **Translation:** T(x, y) -> (x + 3, y - 2)
2. **Reflection:** R_x-axis: (x, y) -> (x, -y)
3. **Rotation:** R(90° clockwise): (x, y) -> (y, -x)
Note: One rule is intentionally incorrect.
### Applying Transformations:
1. **Translation:**
- A(1, 1) -> A'(1 + 3, 1 - 2) = A'(4, -1)
- B(4, 1) -> B'(4 + 3, 1 - 2) = B'(7, -1)
- C(2.5, 3) -> C'(2.5 + 3, 3 - 2) = C'(5.5, 1)
**Coordinates after Translation:**
- A': (4, -1)
- B': (7, -1)
- C': (5.5, 1)
2. **Reflection across the x-axis:**
- A'(4, -1) -> A''(4, 1)
- B'(7, -1) -> B''(7, 1)
- C'(5.5, 1) -> C''(5.5, -1)
**Coordinates after Reflection:**
- A'': (4, 1)
- B'': (7, 1)
- C'': (5.5, -1)
3. **Rotation (90° clockwise):**
- A''(4, 1) -> A'''(1, -4)
- B''(7, 1) -> B'''(1, -7)
- C''(5.5, -1) -> C'''(-1, -5.5)
**Final Image Coordinates after Rotation:**
- A''': (1, -4)
- B''': (1, -7)
- C''': (-1, -5.5)
### Summary of Coordinates
**Pre-Image Coordinates:**
- A: (1, 1)
- B: (4, 1)
- C: (2.5, 3)
**Image Coordinates after Transformation:**
- A''': (1, -4)
- B''': (1, -7)
- C''': (-1, -5.5)
### Drawing the Figure
Since I cannot draw directly in this format, please visualize or sketch the triangle based on the given coordinates. Once transformed, verify the new coordinates to ensure precision.
---
Please provide two classmates' posts for further responses!
Let's create a triangle as our pre-image with the following vertices:
- A(1, 1)
- B(4, 1)
- C(2.5, 3)
The coordinates of the pre-image triangle ABC are:
- A: (1, 1)
- B: (4, 1)
- C: (2.5, 3)
### Transformation Rules:
1. **Translation:** T(x, y) -> (x + 3, y - 2)
2. **Reflection:** R_x-axis: (x, y) -> (x, -y)
3. **Rotation:** R(90° clockwise): (x, y) -> (y, -x)
Note: One rule is intentionally incorrect.
### Applying Transformations:
1. **Translation:**
- A(1, 1) -> A'(1 + 3, 1 - 2) = A'(4, -1)
- B(4, 1) -> B'(4 + 3, 1 - 2) = B'(7, -1)
- C(2.5, 3) -> C'(2.5 + 3, 3 - 2) = C'(5.5, 1)
**Coordinates after Translation:**
- A': (4, -1)
- B': (7, -1)
- C': (5.5, 1)
2. **Reflection across the x-axis:**
- A'(4, -1) -> A''(4, 1)
- B'(7, -1) -> B''(7, 1)
- C'(5.5, 1) -> C''(5.5, -1)
**Coordinates after Reflection:**
- A'': (4, 1)
- B'': (7, 1)
- C'': (5.5, -1)
3. **Rotation (90° clockwise):**
- A''(4, 1) -> A'''(1, -4)
- B''(7, 1) -> B'''(1, -7)
- C''(5.5, -1) -> C'''(-1, -5.5)
**Final Image Coordinates after Rotation:**
- A''': (1, -4)
- B''': (1, -7)
- C''': (-1, -5.5)
### Summary of Coordinates
**Pre-Image Coordinates:**
- A: (1, 1)
- B: (4, 1)
- C: (2.5, 3)
**Image Coordinates after Transformation:**
- A''': (1, -4)
- B''': (1, -7)
- C''': (-1, -5.5)
### Drawing the Figure
Since I cannot draw directly in this format, please visualize or sketch the triangle based on the given coordinates. Once transformed, verify the new coordinates to ensure precision.
---
Please provide two classmates' posts for further responses!
Answered by
GPT-4o mini
Sure! Here’s a more concise version:
### Pre-Image (Triangle ABC):
- A(1, 1)
- B(4, 1)
- C(2.5, 3)
### Transformation Rules (One Incorrect):
1. **Translation:** T(x, y) -> (x + 3, y - 2)
2. **Reflection:** R_x-axis: (x, y) -> (x, -y)
3. **Rotation:** R(90° clockwise): (x, y) -> (y, -x) *(Incorrect)*
### Step-by-Step Transformations:
1. **Translation:**
- A': (4, -1)
- B': (7, -1)
- C': (5.5, 1)
2. **Reflection:**
- A'': (4, 1)
- B'': (7, 1)
- C'': (5.5, -1)
3. **Rotation (90° clockwise):**
- A''': (1, -4)
- B''': (1, -7)
- C''': (-1, -5.5)
### Summary:
**Pre-Image Coordinates:**
- A: (1, 1)
- B: (4, 1)
- C: (2.5, 3)
**Image Coordinates:**
- A''': (1, -4)
- B''': (1, -7)
- C''': (-1, -5.5)
Feel free to ask if you need anything else!
### Pre-Image (Triangle ABC):
- A(1, 1)
- B(4, 1)
- C(2.5, 3)
### Transformation Rules (One Incorrect):
1. **Translation:** T(x, y) -> (x + 3, y - 2)
2. **Reflection:** R_x-axis: (x, y) -> (x, -y)
3. **Rotation:** R(90° clockwise): (x, y) -> (y, -x) *(Incorrect)*
### Step-by-Step Transformations:
1. **Translation:**
- A': (4, -1)
- B': (7, -1)
- C': (5.5, 1)
2. **Reflection:**
- A'': (4, 1)
- B'': (7, 1)
- C'': (5.5, -1)
3. **Rotation (90° clockwise):**
- A''': (1, -4)
- B''': (1, -7)
- C''': (-1, -5.5)
### Summary:
**Pre-Image Coordinates:**
- A: (1, 1)
- B: (4, 1)
- C: (2.5, 3)
**Image Coordinates:**
- A''': (1, -4)
- B''': (1, -7)
- C''': (-1, -5.5)
Feel free to ask if you need anything else!
Answered by
GPT-4o mini
Sure, here’s the example you provided translated into a similar format for the triangle:
### Coordinates:
- A(1, 1)
- B(4, 1)
- C(2.5, 3)
### Transformations:
1. **Translation:** Move **3 units right** and **2 points down.**
2. **Reflection:** Over the **x-axis.**
3. **Rotation:** **Incorrectly** stated as **90° clockwise.**
### Final Coordinates:
- **Pre-Image:**
- A: (1, 1)
- B: (4, 1)
- C: (2.5, 3)
- **Image:**
- A''': (1, -4)
- B''': (1, -7)
- C''': (-1, -5.5)
Let me know if you need further modifications!
### Coordinates:
- A(1, 1)
- B(4, 1)
- C(2.5, 3)
### Transformations:
1. **Translation:** Move **3 units right** and **2 points down.**
2. **Reflection:** Over the **x-axis.**
3. **Rotation:** **Incorrectly** stated as **90° clockwise.**
### Final Coordinates:
- **Pre-Image:**
- A: (1, 1)
- B: (4, 1)
- C: (2.5, 3)
- **Image:**
- A''': (1, -4)
- B''': (1, -7)
- C''': (-1, -5.5)
Let me know if you need further modifications!
Answered by
GPT-4o mini
Certainly! Here’s the triangle example formatted as you requested:
### Coordinates:
- A(1, 1)
- B(4, 1)
- C(2.5, 3)
### Transformations:
- **Translation:** (4, -1), (7, -1), (5.5, 1) (Incorrect)
- **Reflection:** Over the x-axis
- **Rotation:** 90° clockwise (Incorrect)
### Final Image Coordinates:
- A''': (1, -4)
- B''': (1, -7)
- C''': (-1, -5.5)
Let me know if you need any further adjustments!
### Coordinates:
- A(1, 1)
- B(4, 1)
- C(2.5, 3)
### Transformations:
- **Translation:** (4, -1), (7, -1), (5.5, 1) (Incorrect)
- **Reflection:** Over the x-axis
- **Rotation:** 90° clockwise (Incorrect)
### Final Image Coordinates:
- A''': (1, -4)
- B''': (1, -7)
- C''': (-1, -5.5)
Let me know if you need any further adjustments!
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