To write the translation rule for moving triangle \( \triangle GHI \) to triangle \( \triangle G'H'I' \), you need to determine the vector that moves each vertex of triangle \( GHI \) to the corresponding vertex of triangle \( G'H'I' \).
Let's assume the coordinates of the vertices of triangle \( GHI \) are:
- \( G(x_1, y_1) \)
- \( H(x_2, y_2) \)
- \( I(x_3, y_3) \)
And the coordinates of the vertices of triangle \( G'H'I' \) are:
- \( G'(x_1', y_1') \)
- \( H'(x_2', y_2') \)
- \( I'(x_3', y_3') \)
The translation vector can be determined by finding the difference between the coordinates of the corresponding vertices:
-
For vertex \( G \) to \( G' \): \[ \text{Translation vector} = (x_1' - x_1, y_1' - y_1) \]
-
For vertex \( H \) to \( H' \): \[ \text{Translation vector} = (x_2' - x_2, y_2' - y_2) \]
-
For vertex \( I \) to \( I' \): \[ \text{Translation vector} = (x_3' - x_3, y_3' - y_3) \]
For a translation to be uniform, the translation vector should be the same for all three vertices. Therefore, you can apply the translation vector to each vertex of \( \triangle GHI \).
The translation rule can be expressed as: \[ (x, y) \rightarrow (x + a, y + b) \] where \( (a, b) \) is the translation vector that you found, such as \( a = x_1' - x_1 \) and \( b = y_1' - y_1 \).
In summary, the translation rule will generally be: \[ (x, y) \rightarrow (x + a, y + b) \] where \( a \) and \( b \) are the same values computed from one of the vertex translations (usually the first vertex).