To find the coordinates of the vertices after reflecting over the y-axis, we need to take each vertex and apply the reflection transformation.

For a reflection over the y-axis:

• Each x-coordinate changes sign, while the y-coordinate remains the same.

Original Coordinates:

Let's identify the coordinates of points $B$, $C$, and $D$ from the image:

1. Point $B$: $(8, 2)$
2. Point $C$: $(7, 9)$
3. Point $D$: $(5, 5)$

Reflected Coordinates:

1. Point $B'$ after reflection: $(-8, 2)$
2. Point $C'$ after reflection: $(-7, 9)$
3. Point $D'$ after reflection: $(-5, 5)$

Answer:

After reflecting over the y-axis, the new coordinates of the vertices are:

• $B' = (-8, 2)$
• $C' = (-7, 9)$
• $D' = (-5, 5)$

Would you like a detailed explanation of the reflection process?

Here are some related questions to explore further:

1. What are the coordinates of vertices if we reflect them over the x-axis instead?
2. How do we perform a reflection over the line $y = x$?
3. How does reflecting over both axes affect the coordinates?
4. Can we use matrix transformations for reflections? If so, how?
5. How does reflecting over a non-axis line (e.g., $y = -x$) affect points?

Tip: For any reflection, only the coordinates relative to the reflection line change—coordinates perpendicular to that line stay the same.