Question

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?(1 point)The value of h is and the value of k is .

Answer 1

To determine the values of \( h \) and \( k \) in the functions \( f(x) = x + h \) and \( g(y) = y + k \), we first need to understand that these functions describe a translation on the coordinate grid.

1. The function \( f(x) = x + h \) indicates a horizontal translation. Here, \( h \) represents the amount of horizontal movement:
- If \( h > 0 \), the translation is to the right.
- If \( h < 0 \), the translation is to the left.

2. The function \( g(y) = y + k \) indicates a vertical translation. Here, \( k \) represents the amount of vertical movement:
- If \( k > 0 \), the translation is upward.
- If \( k < 0 \), the translation is downward.

To find specific values for \( h \) and \( k \), we would need to know the original coordinates of points \( A \), \( B \), and \( C \) in triangle \( ABC \) and the coordinates of the corresponding points \( A' \), \( B' \), and \( C' \) in triangle \( A'B'C' \).

Once you have the coordinates, you can calculate:
- \( h \) by determining the difference in the x-coordinates from the original triangle to the translated triangle.
- \( k \) by determining the difference in the y-coordinates.

For example, if point \( A \) moves from \( (x_A, y_A) \) to \( (x_{A'}, y_{A'}) \), then:
- \( h = x_{A'} - x_A \)
- \( k = y_{A'} - y_A \)

Without specific coordinates or more details about the translation, we cannot provide exact values for \( h \) and \( k \). If you have the coordinates, please share them and I would be happy to assist you further!