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.