Question
On this coordinate plane, point B is translated to point B'. Which o functions describe the two translations? A: f(x) = x -5 and g(y) + 3
B:f(x) =x +6 and g (y) =y-2 C:f(x) =x -2 and g (y) =y +6
B:f(x) =x +6 and g (y) =y-2 C:f(x) =x -2 and g (y) =y +6
Answers
GPT-4o mini
To determine which functions describe the translations from point B to point B', we need to understand the movements in both the x and y directions.
Here's how to analyze the translations:
1. **Identify the coordinates of point B and point B'.** Without this information, we cannot determine the specific translations. However, you can follow this process with the actual coordinates.
2. **Calculate the change in the x-coordinate:**
- If the x-coordinate of B is \( x_B \) and the x-coordinate of B' is \( x_{B'} \), then the translation in the x-direction can be calculated as:
\[
\text{Translation in x} = x_{B'} - x_B
\]
3. **Calculate the change in the y-coordinate:**
- Similarly, if the y-coordinate of B is \( y_B \) and the y-coordinate of B' is \( y_{B'} \), then the translation in the y-direction can be calculated as:
\[
\text{Translation in y} = y_{B'} - y_B
\]
4. **Translate this into function form**:
- A translation that subtracts from the x-coordinate can be represented as \( f(x) = x - \text{Translation in x} \).
- A translation that adds to the y-coordinate can be represented as \( g(y) = y + \text{Translation in y} \).
Once you calculate the actual movements in both x and y directions from point B to point B', you can match them to the provided options A, B, and C:
- Option A suggests moving left (subtracting 5) and moving up (adding 3).
- Option B suggests moving right (adding 6) and moving down (subtracting 2).
- Option C suggests moving left (subtracting 2) and moving up (adding 6).
So, to select the correct answer:
- Check the calculated translation in the x and y directions against the transformations in the options.
If you provide the coordinates for points B and B', I can help you determine which option corresponds to the translation.
Here's how to analyze the translations:
1. **Identify the coordinates of point B and point B'.** Without this information, we cannot determine the specific translations. However, you can follow this process with the actual coordinates.
2. **Calculate the change in the x-coordinate:**
- If the x-coordinate of B is \( x_B \) and the x-coordinate of B' is \( x_{B'} \), then the translation in the x-direction can be calculated as:
\[
\text{Translation in x} = x_{B'} - x_B
\]
3. **Calculate the change in the y-coordinate:**
- Similarly, if the y-coordinate of B is \( y_B \) and the y-coordinate of B' is \( y_{B'} \), then the translation in the y-direction can be calculated as:
\[
\text{Translation in y} = y_{B'} - y_B
\]
4. **Translate this into function form**:
- A translation that subtracts from the x-coordinate can be represented as \( f(x) = x - \text{Translation in x} \).
- A translation that adds to the y-coordinate can be represented as \( g(y) = y + \text{Translation in y} \).
Once you calculate the actual movements in both x and y directions from point B to point B', you can match them to the provided options A, B, and C:
- Option A suggests moving left (subtracting 5) and moving up (adding 3).
- Option B suggests moving right (adding 6) and moving down (subtracting 2).
- Option C suggests moving left (subtracting 2) and moving up (adding 6).
So, to select the correct answer:
- Check the calculated translation in the x and y directions against the transformations in the options.
If you provide the coordinates for points B and B', I can help you determine which option corresponds to the translation.