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 gy) = y + k that describe the translation. What are the values of h and k in these functions?
(1 point)
functions f(x) = x + h and gy) = y + k that describe the translation. What are the values of h and k in these functions?
(1 point)
Answers
GPT-4o mini
To determine the values of \( h \) and \( k \) for the translation functions \( f(x) = x + h \) and \( g(y) = y + k \), we need to understand how the translation works.
When triangle ABC is translated to produce triangle A' B' C", the coordinates of each vertex of triangle ABC change. If vertex A has coordinates \( (x_A, y_A) \) and it translates to vertex A' with coordinates \( (x_{A'}, y_{A'}) \), then the translation can be described as:
- \( x_{A'} = x_A + h \)
- \( y_{A'} = y_A + k \)
From this, we can express \( h \) and \( k \) as follows:
- \( h = x_{A'} - x_A \)
- \( k = y_{A'} - y_A \)
Thus, \( h \) is the change in the x-coordinate and \( k \) is the change in the y-coordinate as triangle ABC is moved to triangle A' B' C".
To find the specific numerical values of \( h \) and \( k \), you would need the original coordinates of triangle ABC and the new coordinates of triangle A' B' C".
When triangle ABC is translated to produce triangle A' B' C", the coordinates of each vertex of triangle ABC change. If vertex A has coordinates \( (x_A, y_A) \) and it translates to vertex A' with coordinates \( (x_{A'}, y_{A'}) \), then the translation can be described as:
- \( x_{A'} = x_A + h \)
- \( y_{A'} = y_A + k \)
From this, we can express \( h \) and \( k \) as follows:
- \( h = x_{A'} - x_A \)
- \( k = y_{A'} - y_A \)
Thus, \( h \) is the change in the x-coordinate and \( k \) is the change in the y-coordinate as triangle ABC is moved to triangle A' B' C".
To find the specific numerical values of \( h \) and \( k \), you would need the original coordinates of triangle ABC and the new coordinates of triangle A' B' C".