Questions: Jacinda draws triangle ABC and translates it along the coordinate grid to produce triangle A'B'C'. Then, she determines the functions f(x)=x+h and g(y)=y+k that describe the translation. What are the values of h and k in these functions?

Solution Steps

To determine the values of \( h \) and \( k \) in the translation functions \( f(x) = x + h \) and \( g(y) = y + k \), we need to compare the coordinates of the original triangle \( A, B, C \) with the coordinates of the translated triangle \( A', B', C' \). The values of \( h \) and \( k \) represent the horizontal and vertical shifts, respectively.

1. Identify the coordinates of points \( A, B, C \) and their corresponding translated points \( A', B', C' \).
2. Calculate \( h \) as the difference in the x-coordinates of any point and its translated counterpart.
3. Calculate \( k \) as the difference in the y-coordinates of any point and its translated counterpart.

We need to determine the values of \( h \) and \( k \) in the translation functions \( f(x) = x + h \) and \( g(y) = y + k \) that describe the translation of triangle \( ABC \) to triangle \( A'B'C' \).

To find \( h \) and \( k \), we need to compare the coordinates of corresponding points in triangles \( ABC \) and \( A'B'C' \). Let's denote the coordinates of point \( A \) as \( (x_A, y_A) \) and its translated point \( A' \) as \( (x_{A'}, y_{A'}) \). Similarly, we will do this for points \( B \) and \( C \).

The translation functions are given by: \[ f(x) = x + h \] \[ g(y) = y + k \]

This means: \[ x_{A'} = x_A + h \] \[ y_{A'} = y_A + k \]

To find \( h \) and \( k \), we need the coordinates of at least one pair of corresponding points. However, the problem does not provide specific coordinates. We will assume that the problem intends for us to use the given incorrect values as a hint.

The problem states that the value of \( h \) is 0 and the value of \( k \) is 4 is incorrect. This suggests that the correct values are different.

Since we do not have specific coordinates, we can only provide a general solution: \[ h = x_{A'} - x_A \] \[ k = y_{A'} - y_A \]

Final Answer