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To solve this problem, we need to reflect the points \( S \), \( T \), \( U \), and \( V \) over the line \( y = -2 \). Reflection across a horizontal line like \( y = -2 \) affects the \( y \)-coordinates while keeping the \( x \)-coordinates the same.

### Steps to reflect a point across \( y = -2 \):
1. For a point \( (x, y) \), the reflected \( y' \)-coordinate is found by determining how far \( y \) is from \( y = -2 \), and then subtracting or adding that distance to \( -2 \). Mathematically:
   \[
   y' = -2 - (y + 2) = -y - 4
   \]
   So, \( y' = -4 - y \).

### Coordinates of the original vertices:
- \( S(4, 0) \)
- \( T(4, 6) \)
- \( U(6, 6) \)
- \( V(6, 0) \)

### Reflected coordinates:
1. **For \( S(4, 0) \)**:
   - The \( x \)-coordinate remains the same: \( x = 4 \).
   - The \( y \)-coordinate: \( y' = -2 - (0 - (-2)) = -4 \).
   - Reflected \( S' = (4, -4) \).

2. **For \( T(4, 6) \)**:
   - The \( x \)-coordinate remains the same: \( x = 4 \).
   - The \( y \)-coordinate: \( y' = -2 - (6 - (-2)) = -10 \).
   - Reflected \( T' = (4, -10) \).

3. **For \( U(6, 6) \)**:
   - The \( x \)-coordinate remains the same: \( x = 6 \).
   - The \( y \)-coordinate: \( y' = -2 - (6 - (-2)) = -10 \).
   - Reflected \( U' = (6, -10) \).

4. **For \( V(6, 0) \)**:
   - The \( x \)-coordinate remains the same: \( x = 6 \).
   - The \( y \)-coordinate: \( y' = -2 - (0 - (-2)) = -4 \).
   - Reflected \( V' = (6, -4) \).

### Final reflected coordinates:
- \( S'(4, -4) \)
- \( T'(4, -10) \)
- \( U'(6, -10) \)
- \( V'(6, -4) \)

Would you like further details or explanations?

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Here are some related questions:
1. How do you reflect a point over the line \( y = x \)?
2. What is the formula for reflecting a point across the origin?
3. How does reflecting across a vertical line (like \( x = k \)) affect coordinates?
4. What happens when a figure is reflected over the \( x \)-axis?
5. How would you find the reflection over any arbitrary line?

**Tip**: When reflecting over a horizontal or vertical line, only the coordinate perpendicular to that line changes.

Write the coordinates of the vertices after a reflection over the line y = -2 for points S, T, U, and V.

Learn how to reflect the coordinates of vertices S(4, 0), T(4, 6), U(6, 6), and V(6, 0) over the line y = -2. This problem demonstrates key geometric concepts involving reflections on a coordinate plane. Suitable for students in Grades 7-9.

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