Point A on the coordinate plane is translated to point A′, as shown. What are the values of h and k in the translation functions f(x)=x+h and g(y)=y+k?

Answer 1

To determine the values of \( h \) and \( k \) in the translation functions \( f(x) = x + h \) and \( g(y) = y + k \), we first need to identify how point A is translated to point A′.

1. Identify the coordinates: Let's say point A has coordinates \( (x_A, y_A) \) and point A′ has coordinates \( (x_{A'}, y_{A'}) \).

2. Translate the coordinates: The translation functions can be expressed as follows:

   • For the x-coordinate: \[ x_{A'} = x_A + h \] So, we can rearrange to find \( h \): \[ h = x_{A'} - x_A \]
   • For the y-coordinate: \[ y_{A'} = y_A + k \] Similarly, we can find \( k \): \[ k = y_{A'} - y_A \]

3. Calculate \( h \) and \( k \): Using the specific coordinates of A and A′ that you have, substitute them into the equations above to find the values of \( h \) and \( k \).

If you provide the specific coordinates of points A and A′, I can assist you further in calculating the respective values of \( h \) and \( k \).