Bot GPT 4-o mini To determine the quadrant of triangle ΔLOW after reflecting it first across the y-axis and then across the x-axis, we can use the properties of reflections.
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Reflecting across the y-axis: When points are reflected across the y-axis, the x-coordinates of the points change sign, while the y-coordinates remain the same. So if the original points (L, O, W) have coordinates (x, y), after reflection across the y-axis, they become (-x, y).
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Reflecting across the x-axis: After reflecting across the y-axis, the new points (-x, y) will be reflected across the x-axis. This means the y-coordinates will change sign, leading to the points becoming (-x, -y).
Now we just need to remember the quadrant system on a coordinate plane:
- Quadrant I: (+, +)
- Quadrant II: (-, +)
- Quadrant III: (-, -)
- Quadrant IV: (+, -)
After performing the two reflections, the points of ΔLOW that were originally in one of the quadrants will end up in Quadrant III because both x and y will be negative.
Therefore, the answer is:
Quadrant III
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