The problem involves reflecting a set of points over the y-axis. To find the coordinates of the vertices after reflection, we apply the rule for reflecting over the y-axis, which changes the x-coordinate of each point to its opposite (i.e., multiply the x-coordinate by -1) while keeping the y-coordinate the same.

Let’s analyze each vertex:

1. Point B: The original coordinates of $B$ are $(-4, 2)$.

   • Reflection over the y-axis:
     The x-coordinate becomes $4$ (since $-4 \times -1 = 4$), while the y-coordinate remains the same.
     • New coordinates of $B'$: $(4, 2)$.

2. Point C: The original coordinates of $C$ are $(-6, 8)$.

   • Reflection over the y-axis:
     The x-coordinate becomes $6$, while the y-coordinate stays the same.
     • New coordinates of $C'$: $(6, 8)$.

3. Point D: The original coordinates of $D$ are $(-6, -2)$.

   • Reflection over the y-axis:
     The x-coordinate becomes $6$, and the y-coordinate remains $-2$.
     • New coordinates of $D'$: $(6, -2)$.

Summary of the new coordinates:

• $B'(4, 2)$
• $C'(6, 8)$
• $D'(6, -2)$

Would you like further details on reflections, or do you have any other questions?

Here are 5 related questions to explore:

1. How do you reflect a point over the x-axis?
2. What happens when you reflect a point over both the x- and y-axes?
3. How do you find the distance between two points before and after reflection?
4. Can you reflect points over other lines (e.g., y = x)?
5. How would you reflect a figure over a vertical line other than the y-axis?

Tip: When reflecting a point over the y-axis, only the x-coordinate changes, while the y-coordinate remains unaffected!