Answer:
x-axis
Step-by-step explanation:
To determine the line of reflection that maps point \( F(-2, 2) \) to \( F'(-2, -2) \), let's analyze the coordinates of these points.
The reflection of a point across a line results in the point being equidistant from the line on the opposite side.
In this case, point \( F \) is at \( (-2, 2) \) and point \( F' \) is at \( (-2, -2) \).
1. **Reflecting Across a Horizontal Line**:
- The x-coordinates remain the same (both \(-2\)), so the line of reflection must be horizontal.
- The y-coordinates of \( F \) and \( F' \) are \( 2 \) and \(-2\), respectively. The midpoint of these y-coordinates is:
\[
\frac{2 + (-2)}{2} = 0
\]
- Thus, the horizontal line halfway between \( 2 \) and \(-2\) is the x-axis (or \( y = 0 \)).
Let's verify this:
- Reflecting \( F(-2, 2) \) over the x-axis ( \( y = 0 \) ):
- The x-coordinate remains the same: \(-2\).
- The y-coordinate changes to its opposite: \(-2\).
- This maps \( F(-2, 2) \) to \( F'(-2, -2) \).
Since this matches the given image \( F' \), the line of reflection is the **x-axis**.
So, the correct line of reflection is:
**x-axis**