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The question asks for the coordinates of point A after reflecting the quadrilateral across the line \( y = x \).

When a point is reflected across the line \( y = x \), the \( x \)- and \( y \)-coordinates swap places. For example, if the original point is \( (x, y) \), its reflection across \( y = x \) will be \( (y, x) \).

From the diagram, the original coordinates of point A appear to be \( (-6, 2) \).

To reflect this point across the line \( y = x \):
- Swap the \( x \)- and \( y \)-coordinates.
- So, \( (-6, 2) \) becomes \( (2, -6) \).

Thus, the coordinates of \( A' \) are \( (2, -6) \), making the correct answer **B. \( (2, -6) \)**.

Would you like more details or have any further questions?

Here are some related questions:
1. What happens when you reflect a point across the line \( y = -x \)?
2. How do you find the reflection of a point over the x-axis?
3. What are the general transformation rules for reflecting a shape across the origin?
4. How can you calculate the reflection over a vertical line such as \( x = 2 \)?
5. What is the equation of the line of reflection when two points are symmetrical?

**Tip:** To reflect any point across the line \( y = x \), simply swap its coordinates!

The quadrilateral ABCD is to be reflected across the line y = x, as shown in the diagram, to give a new quadrilateral A'B'C'D'. What are the coordinates of A'?

Understand how to reflect a quadrilateral across the line y = x. This example focuses on finding the coordinates of point A' after reflection using key geometry concepts. Suitable for students in Grades 7-9.

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