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To solve the reflection problem:

### Part (a)
When reflecting across the \( y \)-axis, each point's \( x \)-coordinate changes sign while the \( y \)-coordinate remains the same. Let's apply this rule to each point:

1. **Point \( D(2, -5) \)**: Reflecting across the \( y \)-axis changes \( x = 2 \) to \( x = -2 \). So, \( D' = (-2, -5) \).
2. **Point \( E(6, 4) \)**: Changing \( x = 6 \) to \( x = -6 \), we get \( E' = (-6, 4) \).
3. **Point \( F(7, -6) \)**: Changing \( x = 7 \) to \( x = -7 \), we get \( F' = (-7, -6) \).

Thus, the completed coordinates for part (a) are:
- \( D' = (-2, -5) \)
- \( E' = (-6, 4) \)
- \( F' = (-7, -6) \)

### Part (b)
The general rule for reflection across the \( y \)-axis is to map \( (x, y) \) to \( (-x, y) \). Therefore, the correct choice for part (b) is:
- \( (x, y) \rightarrow (-x, y) \)

Would you like further explanation on this reflection process, or do you have any specific questions?

Here are some related questions to expand on this topic:
1. What is the reflection rule for reflecting across the \( x \)-axis?
2. How would the coordinates change if the triangle were reflected across the origin?
3. What is the impact on coordinates when reflecting across the line \( y = x \)?
4. How can you determine the reflection of a shape using a coordinate plane without plotting points?
5. What transformations keep the size and shape of a figure unchanged?

**Tip:** When reflecting over the \( y \)-axis, only the \( x \)-coordinate changes sign, keeping the \( y \)-coordinate the same.

Triangle DEF is reflected across the y-axis. The result is triangle D'E'F'. Determine the new coordinates of points D, E, and F after reflection and choose the general rule for reflecting across the y-axis.

Explore how to reflect triangle DEF across the y-axis, find the coordinates of points D, E, and F after reflection, and learn the general rule for reflections across the y-axis. This problem covers core geometry concepts suitable for Grades 7-9.

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