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Let's break down the examples in your image.

### Example 5:
- **Reflection of triangle \( \Delta PQR \) over the line \( y = -x \)**.
- The reflection rule for reflecting over \( y = -x \) is to switch the coordinates and negate both: \( (x, y) \to (-y, -x) \).
- Applying this rule to each point:
  - \( P(-1, 2) \) becomes \( P'(-2, 1) \)
  - \( Q(3, 1) \) becomes \( Q'(-1, -3) \)
  - \( R(2, -2) \) becomes \( R'(-2, -2) \)

### Example 6:
- **Reflection of triangle \( \Delta EFG \) over the line \( x = 1 \)**.
- To reflect a point over the line \( x = 1 \), we calculate the horizontal distance from each point to the line and move it the same distance on the opposite side.
  - For \( E(-4, 6) \), the distance to \( x = 1 \) is 5 units. The reflected point is \( E'(6, 6) \).
  - For \( F(1, 6) \), the distance is 0, so \( F \) remains at \( F'(1, 6) \).
  - For \( G(-2, -2) \), the distance to \( x = 1 \) is 3 units. The reflected point is \( G'(4, -2) \).

### Example 7:
- **Transformation rule for \( \Delta ABC \) to \( \Delta A'B'C' \)**.
- We can observe that each point is reflected across the \( y \)-axis, meaning the transformation rule is a reflection over the \( y \)-axis: \( (x, y) \to (-x, y) \).
  - \( A(4, 0) \to A'(-4, 0) \)
  - \( B(-7, -5) \to B'(7, -5) \)
  - \( C(2, 6) \to C'(-2, 6) \)

Would you like more details or have any questions?

### Related Questions:
1. How do we determine the reflection rule for other lines like \( y = x \)?
2. What changes when reflecting across lines other than the axes?
3. How can we verify if a point has been reflected correctly?
4. Can we derive a formula for any reflection over arbitrary lines?
5. How are reflections related to symmetry in geometry?

**Tip**: Always visualize the reflection by counting the distance from the point to the reflection line!

Example 5: ΔPQR reflected over the line y = -x. What is the general rule for reflecting across y = -x? Example 6: Reflect ΔEFG over the line x = 1. Example 7: What rule represents the transformation for ΔABC to ΔA'B'C'?

Learn how to reflect triangles ΔPQR, ΔEFG, and ΔABC over lines such as y = -x, x = 1, and the y-axis. This problem involves key geometric concepts such as reflections, transformations, and coordinate plane geometry. Suitable for students in Grades 8-10.

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