To solve this problem, we are tasked with finding the coordinates of the vertices of the shape after a reflection over the line $y = x$.

Steps to Solve:

1. Understanding Reflection Over $y = x$:

   • When reflecting a point over the line $y = x$, the coordinates of the point $(x, y)$ are swapped. The new coordinates become $(y, x)$.

2. Identify the Vertices: From the grid, the vertices of the original shape are:

   • $F = (-8, 8)$
   • $E = (-3, 8)$
   • $D = (-3, -3)$
   • $C = (-8, -3)$

3. Apply the Reflection Rule: For each point $(x, y)$, swap $x$ and $y$:

   • $F' = (8, -8)$
   • $E' = (8, -3)$
   • $D' = (-3, -3)$
   • $C' = (-3, -8)$

Reflected Coordinates:

After the reflection over $y = x$, the coordinates of the vertices are:

• $F' = (8, -8)$
• $E' = (8, -3)$
• $D' = (-3, -3)$
• $C' = (-3, -8)$

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. What happens to the coordinates when reflecting over the line $y = -x$?
2. How do you verify if the reflection was performed correctly?
3. Can you describe how reflections over other lines (like $y = 0$ or $x = 0$) are performed?
4. What is the distance between the original points and their reflected images?
5. How would the shape look if it were reflected over the $x$-axis instead?

Tip: Always double-check your reflections by plotting both the original and reflected points on the graph!