Question
A coordinate plane shows two plotted triangles, upper A upper B upper C, and upper A prime upper B prime upper C prime in the same orientation. Both axes range from negative 7 to 7 in increments of 1.
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
.
Answers
GPT-4o mini
To determine the values of \( h \) and \( k \) in the functions \( f(x) = x + h \) and \( g(y) = y + k \) that describe the translation from triangle \( ABC \) to triangle \( A'B'C' \), you need to find the horizontal and vertical translations.
1. **Find the Coordinates of Triangle ABC:**
Identify the coordinates of the vertices \( A \), \( B \), and \( C \) of triangle \( ABC \).
2. **Find the Coordinates of Triangle A'B'C':**
Identify the coordinates of the corresponding vertices \( A' \), \( B' \), and \( C' \) of the translated triangle \( A'B'C' \).
3. **Calculate the Translation for h and k:**
- For \( h \), use the formula \( h = x' - x \), where \( (x', y') \) are the coordinates of the translated point and \( (x, y) \) are the original coordinates.
- For \( k \), use the formula \( k = y' - y \).
You would typically calculate these differences for one of the corresponding points (either for vertex \( A \) and \( A' \), vertex \( B \) and \( B' \), or vertex \( C \) and \( C' \)), as long as the translation applies consistently to each vertex.
If you provide the specific coordinates of the triangles \( A \), \( B \), \( C \) and \( A' \), \( B' \), \( C' \), I can help you calculate the values of \( h \) and \( k \).
1. **Find the Coordinates of Triangle ABC:**
Identify the coordinates of the vertices \( A \), \( B \), and \( C \) of triangle \( ABC \).
2. **Find the Coordinates of Triangle A'B'C':**
Identify the coordinates of the corresponding vertices \( A' \), \( B' \), and \( C' \) of the translated triangle \( A'B'C' \).
3. **Calculate the Translation for h and k:**
- For \( h \), use the formula \( h = x' - x \), where \( (x', y') \) are the coordinates of the translated point and \( (x, y) \) are the original coordinates.
- For \( k \), use the formula \( k = y' - y \).
You would typically calculate these differences for one of the corresponding points (either for vertex \( A \) and \( A' \), vertex \( B \) and \( B' \), or vertex \( C \) and \( C' \)), as long as the translation applies consistently to each vertex.
If you provide the specific coordinates of the triangles \( A \), \( B \), \( C \) and \( A' \), \( B' \), \( C' \), I can help you calculate the values of \( h \) and \( k \).