To determine the final location of triangle ΔLOW after reflecting it first across the y-axis and then across the x-axis, we need to analyze the transformations step by step.
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Reflecting across the y-axis: This transformation changes the x-coordinates of all points. If a point \( (x, y) \) is reflected across the y-axis, it becomes \( (-x, y) \).
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Reflecting across the x-axis: This transformation changes the y-coordinates of all points. If a point \( (x, y) \) is reflected across the x-axis, it becomes \( (x, -y) \).
Let's denote the vertices of ΔLOW:
- L (x1, y1)
- O (x2, y2)
- W (x3, y3)
After the first reflection across the y-axis:
- L becomes (-x1, y1)
- O becomes (-x2, y2)
- W becomes (-x3, y3)
After the second reflection across the x-axis:
- L becomes (-x1, -y1)
- O becomes (-x2, -y2)
- W becomes (-x3, -y3)
Now, the final coordinates will have:
- For any point (-xi, yi), the new coordinate will be (-xi, -yi).
Next, let's analyze the location of these transformed points:
- If the original points (L, O, W) were in the first quadrant, their new coordinates after the transformations will move them to the third quadrant.
- If the original points were in the second quadrant, they will also move to the third quadrant.
- If the original points were in the third quadrant, they will move to the first quadrant after both reflections.
- If the original points were in the fourth quadrant, they will move to the second quadrant after both reflections.
Since the question doesn't specify the original positions of points L, O, and W, we can't pinpoint the original quadrant they may have started from. However, regardless of whether they initially started in the first, second, third, or fourth quadrant, the net result of the two reflections will lead them to a determined final quadrant.
Given the case described, the most important point to insight is that reflecting twice causes a directional flip across both axes.
Thus, after computing the successive reflections, while it's likely the case that every adjustment in position should be mapped, the final conclusion can succinctly state that after two reflections across both axes, any set of points will appear in either Quadrant I or Quadrant III.
Since the points originally plotted formulated a triangle (and thus reasonably assuming they could sum out to an inclusive area), without explicit coordinates, we wouldn't logically pin this as a defined choice falling in Quadrant I, through logically concluding they transform through Quadrant II upon processing negative to positive.
Hence, all said, the outcome of the set will unfailingly lead into Quadrant III after reflecting across both axes.
Final Answer: Quadrant III.