To find the two moves that could replace the one translation from Triangle LOW to Triangle L"O"W", we first need to analyze the coordinates of the points in each triangle.
Given the coordinates:
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Triangle LOW:
- L: (-5, -2)
- O: (-2, -4)
- W: (-4, -6)
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Triangle L"O"W":
- L": (-5, 10)
- O": (-2, 8)
- W": (-4, 6)
Step 1: Translation Analysis
To see how the points have changed with respect to translation, we can note down the changes in the y-coordinates since the x-coordinates of L and L" remain the same (-5) and O and O" as well as W and W" are consistent in x-coordinates.
- For L to L":
- Change in y: 10 - (-2) = 12
- For O to O":
- Change in y: 8 - (-4) = 12
- For W to W":
- Change in y: 6 - (-6) = 12
Thus, the translation can be characterized as moving up by 12 units in the y-direction.
Step 2: Finding Alternative Transformations
Since the translation involves moving points vertically, we should consider transformations that can also accomplish a vertical upward shift.
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Reflection across a line parallel to the x-axis (horizontal line) would effectively reflect the points across such a line, effectively allowing for a positioning that could include an upward move as needed.
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Reflection across a line that is not horizontal could also facilitate the necessary repositioning alongside other transformations. But considering perpendicular lines could lead to desired altitude adjustment too.
Given the operations, we need one transformation that matches shifting the y-values effectively by fixed distances.
Conclusion
The two moves that could replace the one translation in this specific case are likely:
- A reflection across parallel lines. This would retain some properties of height for respective upward adjustments as required.
- A subsequent reflection across perpendicular lines which could provide another adjustment to the necessary positions vertically needed post the parallel adjustments if necessary.
So the final answer would likely lean toward these two choices. However, the most coherent adjustment to the translation based on the vertical output would lead strongly towards the reflections as described, ensuring vertical shifts as needed through perpendicular or parallel lines.