To solve this problem, we need to find the coordinates of the vertices $B'$, $C'$, and $D'$ after reflecting the points $B$, $C$, and $D$ over the line $y = x$.

Key Concept: Reflection over the line $y = x$

When a point $(x, y)$ is reflected over the line $y = x$, the coordinates of the point become $(y, x)$. In other words, you simply swap the $x$- and $y$-coordinates.

Coordinates of the original points:

From the graph:

• $B(0, 2)$
• $C(10, 0)$
• $D(8, -6)$

Reflected Coordinates:

1. $B(0, 2)$ reflects to $B'(2, 0)$
2. $C(10, 0)$ reflects to $C'(0, 10)$
3. $D(8, -6)$ reflects to $D'(-6, 8)$

Thus, the coordinates of the reflected points are:

• $B'(2, 0)$
• $C'(0, 10)$
• $D'(-6, 8)$

Would you like further clarification or details? Here are some related questions:

1. What are the general rules for reflecting a point over different lines like $y = -x$?
2. How does reflecting over the line $y = x$ affect geometric shapes?
3. How can you determine the equation of a line of reflection given a set of original and reflected points?
4. How does reflecting over the line $y = x$ relate to rotations and translations in the coordinate plane?
5. How do the distances between points and lines of reflection compare before and after a reflection?

Tip: Reflection over the line $y = x$ is useful when analyzing symmetry and transformations in geometry.