Question

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 \( k \).