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 need to know the coordinates of points \( A \) and \( A' \).

1. **Identify the Coordinates:**
Let's assume that the coordinates of point \( A \) are \( (x_1, y_1) \) and the coordinates of point \( A' \) are \( (x_2, y_2) \).

2. **Calculate \( h \) and \( k \):**
- The translation for the x-coordinate can be represented as:
\[
x_2 = x_1 + h \quad \Rightarrow \quad h = x_2 - x_1
\]
- The translation for the y-coordinate can be represented as:
\[
y_2 = y_1 + k \quad \Rightarrow \quad k = y_2 - y_1
\]

3. **Substituting the Values:**
- If you replace \( x_1 \), \( y_1 \), \( x_2 \), and \( y_2 \) with the actual coordinates obtained from the points, you will get the numerical values for \( h \) and \( k \).

If you can provide the specific coordinates for points \( A \) and \( A' \), I can help you compute \( h \) and \( k \) directly.