To determine the coordinates of vertex X' after reflecting point X over a horizontal line, we first need to identify the y-coordinate of point X and understand how reflection works.
The coordinates of point X are given as (-3, 9). When reflecting over a horizontal line, the x-coordinate remains unchanged while the y-coordinate is transformed. Specifically, if the horizontal line of reflection is at y = k, the new y-coordinate (let's call it \( y' \)) is calculated using the formula:
\[ y' = k - (y - k) = 2k - y \]
To solve this problem, we need to establish the line of reflection. Since the line is horizontal and the specific line is not provided, we can assume that the reflection occurs over the x-axis (y = 0) as a common example.
If the reflection is over the x-axis, the y-coordinate transformation simplifies as follows:
- When reflecting over the x-axis, we multiply the y-coordinate by -1.
For point X (-3, 9), the reflection over the x-axis gives:
\[ X' = (-3, -9) \]
So, the coordinates of vertex X' after reflecting over the x-axis are (-3, -9).
Looking at the provided answer choices, the correct coordinates for vertex X' is:
D. (-3,-9).
1 answer