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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.

Write the coordinates of the vertices after a reflection over the line y = x.

Learn how to reflect points over the line y = x. This geometry problem demonstrates the reflection transformation of vertices B, C, and D. Suitable for students in Grades 7-10.

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