Point A (2,2)on the coordinate plane is translated to point A′ (-3,1), as shown. What are the values of h and k in the translation functions f(x)=x+h and g(y)=y+k?(1 point)

Answer 1

To find the values of \( h \) and \( k \) in the translation functions \( f(x) = x + h \) and \( g(y) = y + k \), we'll analyze the translation from point \( A(2, 2) \) to point \( A'(-3, 1) \).

1. For the x-coordinates: \[ x' = x + h \] In this case: \[ -3 = 2 + h \] Solving for \( h \): \[ h = -3 - 2 = -5 \]

2. For the y-coordinates: \[ y' = y + k \] In this case: \[ 1 = 2 + k \] Solving for \( k \): \[ k = 1 - 2 = -1 \]

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