To determine the quadrant of each reflected ordered pair, we need to apply the rules of reflection.
- Reflection across the y-axis: The x-coordinate changes its sign, while the y-coordinate remains the same. Thus, (x, y) becomes (-x, y).
- Reflection across the x-axis: The x-coordinate remains the same, while the y-coordinate changes its sign. Thus, (x, y) becomes (x, -y).
Now, let's evaluate each ordered pair:
-
(-2, 8) reflected across the y-axis:
- Reflection: (2, 8)
- Location: Quadrant I (positive x and positive y)
-
(-6, -1) reflected across the x-axis:
- Reflection: (-6, 1)
- Location: Quadrant II (negative x and positive y)
-
(-3, 5) reflected across the y-axis:
- Reflection: (3, 5)
- Location: Quadrant I (positive x and positive y)
-
(-5, 5) reflected across the x-axis:
- Reflection: (-5, -5)
- Location: Quadrant III (negative x and negative y)
-
(7, 1) reflected across the x-axis:
- Reflection: (7, -1)
- Location: Quadrant IV (positive x and negative y)
-
(-3, -9) reflected across the y-axis:
- Reflection: (3, -9)
- Location: Quadrant IV (positive x and negative y)
Now summarizing the locations:
- (-2, 8) → Quadrant I
- (-6, -1) → Quadrant II
- (-3, 5) → Quadrant I
- (-5, 5) → Quadrant III
- (7, 1) → Quadrant IV
- (-3, -9) → Quadrant IV
In summary:
- Quadrant I: (2, 8), (3, 5)
- Quadrant II: (-6, 1)
- Quadrant III: (-5, -5)
- Quadrant IV: (7, -1), (3, -9)