https://file.aiquickdraw.com/mathbot/file/17262074898450ribpkr2.jpg

The problem asks to reflect the triangle \( \Delta RST \) over the line \( y = -x \). Let's break down the process for reflecting each point of the triangle:

1. **Reflection over the line \( y = -x \):** To reflect a point \( (x, y) \) over the line \( y = -x \), the coordinates of the reflected point become \( (-y, -x) \).

Now, let’s find the reflected coordinates of each point \( R \), \( S \), and \( T \):

- The coordinates of \( R \) appear to be \( (-4, 3) \). When reflected over \( y = -x \), its new coordinates become \( (-3, 4) \).
- The coordinates of \( S \) appear to be \( (2, -6) \). When reflected, the new coordinates become \( (6, -2) \).
- The coordinates of \( T \) appear to be \( (-6, -6) \). When reflected, the new coordinates become \( (6, 6) \).

Now, plot the new points \( R'(-3, 4) \), \( S'(6, -2) \), and \( T'(6, 6) \) to form the reflected triangle.

Would you like me to assist further with plotting these points or any other part of the process?

Here are 5 relative questions for further exploration:
1. What is the general rule for reflecting over the line \( y = x \)?
2. How do you reflect points over the origin?
3. How does reflecting over different lines affect the orientation of a shape?
4. How would the reflection differ if we reflected over the y-axis instead?
5. How can you determine the equation of a line of symmetry for a given figure?

**Tip:** When reflecting over lines like \( y = -x \), always remember to swap and negate the coordinates.

Graph the image of triangle ΔRST after a reflection over the line y = -x.

This problem covers how to reflect triangle ΔRST over the line y = -x. The coordinates of each vertex are transformed according to the formula (x, y) -> (-y, -x). This exercise focuses on reflections and transformations in coordinate geometry, ideal for students in Grades 8-10.

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