To determine the sequence of rigid transformations that maps triangle ABCD to triangle A"B"C"D", we need to identify the transformations needed, which could include translations, reflections, and rotations.
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Reflection: If we reflect across the y-axis, the transformation would change the coordinates of any point \( (x, y) \) to \( (-x, y) \).
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Translation: After reflection, we may need to translate the transformed figure. For example, if we want to move the figure 4 units to the left, the transformation would change the coordinates to \( (-x - 4, y) \).
Therefore, the composition of transformations that would map ABCD to A"B"C"D" can be described as:
- Reflect across the y-axis: \( (x, y) \rightarrow (-x, y) \)
- Translate left by 4 units: \( (-x, y) \rightarrow (-x - 4, y) \)
The overall transformation can be written as: \[ (x, y) \rightarrow (-x - 4, y) \]
This matches the first option given in the responses:
- \((x,y) \rightarrow (-x - 4, y)\)
Thus, the correct answer is: \[ \textbf{(x,y)→(−x−4,y)} \]
3 answers