Question
On this coordinate plane, point A is translated into point A′. Which functions give the two translations?
Responses
f(x)=x−5 and g(y)=y−2
f of x is equal to x minus 5 and g of y is equal to y minus 2 - no response given
f(x)=x+2 and g(y)=y+5
f of x is equal to x plus 2 and g of y is equal to y plus 5 - no response given
f(x)=x+5 and g(y)=y+2
f of x is equal to x plus 5 and g of y is equal to y plus 2 - no response given
f(x)=x+6 and g(y)=y+3
Responses
f(x)=x−5 and g(y)=y−2
f of x is equal to x minus 5 and g of y is equal to y minus 2 - no response given
f(x)=x+2 and g(y)=y+5
f of x is equal to x plus 2 and g of y is equal to y plus 5 - no response given
f(x)=x+5 and g(y)=y+2
f of x is equal to x plus 5 and g of y is equal to y plus 2 - no response given
f(x)=x+6 and g(y)=y+3
Answers
GPT-4o mini
To determine which functions correspond to the translations from point A to A′ on the coordinate plane, we need to identify the changes in the x and y coordinates from point A to point A′.
Let's evaluate the provided functions step by step:
1. If the x-coordinate of A is translated to A′ by a certain value, that means there is a function \( f(x) \) that represents this translation.
2. Similarly, if the y-coordinate of A is translated to A′ by another value, there will be a function \( g(y) \) for this translation.
Now, let’s examine each response to see which set of translation functions makes sense given a general translation:
1. **Response 1**:
- \( f(x) = x - 5 \) and \( g(y) = y - 2 \)
- This means the x-coordinate is decreased by 5 and the y-coordinate is decreased by 2.
2. **Response 2**:
- \( f(x) = x + 2 \) and \( g(y) = y + 5 \)
- This means the x-coordinate is increased by 2 and the y-coordinate is increased by 5.
3. **Response 3**:
- \( f(x) = x + 5 \) and \( g(y) = y + 2 \)
- This means the x-coordinate is increased by 5 and the y-coordinate is increased by 2.
4. **Response 4**:
- \( f(x) = x + 6 \) and \( g(y) = y + 3 \)
- This means the x-coordinate is increased by 6 and the y-coordinate is increased by 3.
To select among these, compare the coordinates of points A and A′:
- If point A is at \( (a, b) \) and point A′ is at \( (a + m, b + n) \), we can determine \( m \) and \( n \). The appropriate functions will be:
- \( f(x) = x + m \)
- \( g(y) = y + n \)
Make sure to calculate \( m \) and \( n \) based on the specific coordinates of points A and A′ you have if they are provided. Without the specific coordinates, we can't definitively choose a correct response. However, any of the functions listed can be correct based on the nature and direction of the translation.
If you can provide the coordinates of points A or A′, we could pinpoint the correct translation functions!
Let's evaluate the provided functions step by step:
1. If the x-coordinate of A is translated to A′ by a certain value, that means there is a function \( f(x) \) that represents this translation.
2. Similarly, if the y-coordinate of A is translated to A′ by another value, there will be a function \( g(y) \) for this translation.
Now, let’s examine each response to see which set of translation functions makes sense given a general translation:
1. **Response 1**:
- \( f(x) = x - 5 \) and \( g(y) = y - 2 \)
- This means the x-coordinate is decreased by 5 and the y-coordinate is decreased by 2.
2. **Response 2**:
- \( f(x) = x + 2 \) and \( g(y) = y + 5 \)
- This means the x-coordinate is increased by 2 and the y-coordinate is increased by 5.
3. **Response 3**:
- \( f(x) = x + 5 \) and \( g(y) = y + 2 \)
- This means the x-coordinate is increased by 5 and the y-coordinate is increased by 2.
4. **Response 4**:
- \( f(x) = x + 6 \) and \( g(y) = y + 3 \)
- This means the x-coordinate is increased by 6 and the y-coordinate is increased by 3.
To select among these, compare the coordinates of points A and A′:
- If point A is at \( (a, b) \) and point A′ is at \( (a + m, b + n) \), we can determine \( m \) and \( n \). The appropriate functions will be:
- \( f(x) = x + m \)
- \( g(y) = y + n \)
Make sure to calculate \( m \) and \( n \) based on the specific coordinates of points A and A′ you have if they are provided. Without the specific coordinates, we can't definitively choose a correct response. However, any of the functions listed can be correct based on the nature and direction of the translation.
If you can provide the coordinates of points A or A′, we could pinpoint the correct translation functions!