To determine the correct mapping notation for reflecting a figure across the y-axis, let's understand the effect such a reflection has on the coordinates of points in the figure:
1. Identifying the Reflection Rule:
- When you reflect a point across the y-axis, the x-coordinate of the point changes sign (i.e., it gets negated), but the y-coordinate remains unchanged. This is because the y-axis is the vertical axis, and reflection over it does not change the vertical position (y-coordinate) but reverses the horizontal position (x-coordinate).
2. Analyzing Each Option:
- Option 1: [tex]\((x, y) \rightarrow (-x, y)\)[/tex]
- This notation indicates that the x-coordinate is negated, while the y-coordinate remains the same.
- This matches our rule for reflecting over the y-axis.
- Option 2: [tex]\((x, y) \rightarrow (x, -y)\)[/tex]
- This notation indicates that the x-coordinate stays the same, while the y-coordinate is negated.
- This represents reflection over the x-axis, not the y-axis.
- Option 3: [tex]\((x, y) \rightarrow (-x, -y)\)[/tex]
- This notation indicates that both the x-coordinate and y-coordinate are negated.
- This represents a reflection through the origin, not specifically over the y-axis.
- Option 4: [tex]\((x, y) \rightarrow (y, x)\)[/tex]
- This notation indicates that the coordinates are swapped.
- This doesn't reflect any standard axis reflection and is not relevant to our question about reflection over the y-axis.
3. Conclusion:
Based on this analysis, the correct mapping notation for reflecting a figure across the y-axis is:
[tex]\[
(x, y) \rightarrow (-x, y)
\][/tex]
So, Marissa should use:
[tex]\[
(x, y) \rightarrow (-x, y)
\][/tex]
