To determine which two moves could replace the translation from triangle LOW to triangle L"O"W", we first need to analyze the transformation.
Points of Triangle LOW:
- L: (-5, -2)
- O: (-2, -4)
- W: (-4, -6)
Points of Triangle L"O"W":
- L": (-5, 10)
- O": (-2, 8)
- W": (-4, 6)
Step 1: Identify the translation vector
To get from each point of triangle LOW to triangle L"O"W", we will look at the changes in the y-coordinates:
- L: from -2 to 10 (increase of 12)
- O: from -4 to 8 (increase of 12)
- W: from -6 to 6 (increase of 12)
The translation moves each y-coordinate up by 12 units, staying in the same x-coordinates.
Step 2: Explore possible moves
Now let's denote the possible choices:
- A. a reflection across intersecting lines
- B. a counterclockwise rotation of 180 degrees
- C. a reflection across perpendicular lines
- D. a reflection across parallel lines
Analysis of Two Moves
Since the translation is a consistent vertical shift, we need a combination of transformations that can jointly produce the outcome of translating all points upward in a consistent manner.
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A Reflection across intersecting lines generally changes both x and y coordinates in a non-linear way, making this improbable.
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B Counterclockwise rotation of 180 degrees will rotate each point around the origin, which will change both coordinates, thus this option does not seem to work.
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C Reflection across perpendicular lines could involve sequential transformations, but aligning them perfectly to match the upward shift in y-coordinates is complex and potentially does not yield the same outcome.
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D Reflection across parallel lines followed by another transformation could align the points vertically without affecting their horizontal alignment.
Possible Conclusion
Based on the transformation characteristics and the requirement to achieve the same effect through two moves it would most feasibly be (D) since reflecting across a parallel line could catch the upward shift and then potentially another transformation could align it correctly.
Thus, the correct choice would be: D. a reflection across parallel lines.
Final Assertion
To verify further, we can also consider practical attempts or geometric tools, but for theoretical reasoning, the reasoning points toward option D as the most valid route to match the output of the translation described.