Question

Point A (2, 2) is translated to Point A' (-3, 1) what are the values of h and k in the translation functions f (x) = x + h and g (y) = y + k

Answer 1

To find the values of \( h \) and \( k \) for the translation functions \( f(x) = x + h \) and \( g(y) = y + k \), we need to determine how the x and y coordinates of Point A (2, 2) are transformed to reach Point A' (-3, 1).

1. **Translation in the x-direction:**
- Initial x-coordinate: \( 2 \)
- Translated x-coordinate: \( -3 \)
- Set up the equation using the translation function:
\[
-3 = 2 + h
\]
- Solving for \( h \):
\[
h = -3 - 2 = -5
\]

2. **Translation in the y-direction:**
- Initial y-coordinate: \( 2 \)
- Translated y-coordinate: \( 1 \)
- Set up the equation using the translation function:
\[
1 = 2 + k
\]
- Solving for \( k \):
\[
k = 1 - 2 = -1
\]

Thus, the values of \( h \) and \( k \) are:
- \( h = -5 \)
- \( k = -1 \)

So the translation functions can be expressed as \( f(x) = x - 5 \) and \( g(y) = y - 1 \).