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To find the lines of reflection that will flip the given figure onto itself, we need to identify both horizontal and vertical lines that divide the figure symmetrically.

### Points given:
- \( A(-4, 3) \)
- \( B(5, 3) \)
- \( C(5, -2) \)
- \( D(-4, -2) \)

### Step 1: Reflection over the vertical line
The horizontal distance between \( A \) and \( B \) is 9 units (from \( x = -4 \) to \( x = 5 \)). The vertical line of reflection should pass through the midpoint of this distance. The midpoint can be calculated as:

\[
\text{Midpoint on the x-axis} = \frac{-4 + 5}{2} = \frac{1}{2} = 0.5
\]

So, the vertical line of reflection is at \( x = 0.5 \).

### Step 2: Reflection over the horizontal line
Similarly, the vertical distance between points \( A \) and \( D \) is 5 units (from \( y = 3 \) to \( y = -2 \)). The horizontal line of reflection should pass through the midpoint of this distance. The midpoint on the y-axis is:

\[
\text{Midpoint on the y-axis} = \frac{3 + (-2)}{2} = \frac{1}{2} = 0.5
\]

So, the horizontal line of reflection is at \( y = 0.5 \).

### Final Answer:
- The vertical line of reflection is \( x = 0.5 \).
- The horizontal line of reflection is \( y = 0.5 \).

Let me know if you would like further details or clarification. 

### Related Questions:
1. How do we find the equation of the line of reflection between two points?
2. What is the reflection formula for points across the y-axis?
3. Can the reflection lines always be fractional?
4. What would happen to the shape if it was reflected over a diagonal line?
5. How can we use reflections to verify symmetry in polygons?

**Tip:** When finding reflection lines, always look for midpoints between corresponding vertices.

Complete the equations identifying both lines of reflection that will flip the given figure onto itself. The lines of reflection are x = ___ and y = ___.

Learn how to find the lines of reflection for a given geometric figure. This problem involves using the midpoint formula to find the vertical and horizontal lines of reflection, focusing on symmetry and geometry concepts. Suitable for students in Grades 8-10.

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