To find the sequence of transformations that maps triangle \( \Delta ABC \) to triangle \( \Delta A"B"C" \), we need to analyze the transformations involved.
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Reflection: Triangle \( \Delta ABC \) is reflected across the x-axis, which changes the sign of the y-coordinate. This can be represented as: \[ (x, y) \rightarrow (x, -y) \]
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Translation: After the reflection, the triangle is translated 4 units up. This is expressed as: \[ (x, y) \rightarrow (x, y + 4) \] however, since the reflection already flipped the triangle and shifted it down in the process, we would adjust both components after reflection.
So the combined transformation would first reflect across the x-axis and then, to move it correctly, we would translate upwards.
Putting these together, the transformation to carry \( \Delta ABC \) to \( \Delta A"B"C" \) is a reflection followed by a vertical translation.
Looking at your options, the correct transformation that relocates the triangle correctly would be: \[ (x, y) \rightarrow (x + 4, -y) \] This effectively combines both the reflection and the upward movement accurately as per the problem.
Thus, the answer is: \[ \boxed{(x,y) \rightarrow (x + 4, -y)} \]
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