Question
On this coordinate plane, point A is translated into point A′. A is (-2,3) A' is (3,5) Which functions give the two translations?(1 point)Responsesf(x)=x+5 and g(y)=y+2f left parenthesis x right parenthesis equals x plus 5 and g left parenthesis y right parenthesis equals y plus 2f(x)=x+6 and g(y)=y+3f left parenthesis x right parenthesis equals x plus 6 and g left parenthesis y right parenthesis equals y plus 3f(x)=x−5 and g(y)=y−2f left parenthesis x right parenthesis equals x minus 5 and g left parenthesis y right parenthesis equals y minus 2f(x)=x+2 and g(y)=y+5
Answers
GPT-4o mini
To find the translation from point A (-2, 3) to point A' (3, 5), we need to determine how the x-coordinate and y-coordinate change.
1. **For the x-coordinate**:
- A(-2) translates to A'(3).
- The change in x is: \( 3 - (-2) = 3 + 2 = 5 \).
- This means that the function for x is: \( f(x) = x + 5 \).
2. **For the y-coordinate**:
- A(3) translates to A'(5).
- The change in y is: \( 5 - 3 = 2 \).
- This means that the function for y is: \( g(y) = y + 2 \).
Putting it together, the two translation functions are:
- \( f(x) = x + 5 \)
- \( g(y) = y + 2 \)
Therefore, the correct response is:
**f(x) = x + 5 and g(y) = y + 2**.
1. **For the x-coordinate**:
- A(-2) translates to A'(3).
- The change in x is: \( 3 - (-2) = 3 + 2 = 5 \).
- This means that the function for x is: \( f(x) = x + 5 \).
2. **For the y-coordinate**:
- A(3) translates to A'(5).
- The change in y is: \( 5 - 3 = 2 \).
- This means that the function for y is: \( g(y) = y + 2 \).
Putting it together, the two translation functions are:
- \( f(x) = x + 5 \)
- \( g(y) = y + 2 \)
Therefore, the correct response is:
**f(x) = x + 5 and g(y) = y + 2**.