https://file.aiquickdraw.com/mathbot/file/1726096452879rzpgdim7.jpg

The problem involves a triangle \( STU \) with vertices at \( S(-1, -6) \), \( T(0, -3) \), and \( U(3, -4) \). It asks to reflect this triangle over the line \( y = -x \), which typically involves switching the coordinates and changing the signs of the original points.

To perform the reflection of each vertex across the line \( y = -x \), the transformation rule is:

\[
(x, y) \rightarrow (-y, -x)
\]

Applying this rule to each vertex:

1. For \( S(-1, -6) \), the reflection will be:
   \[
   (-1, -6) \rightarrow (6, 1)
   \]
   
2. For \( T(0, -3) \), the reflection will be:
   \[
   (0, -3) \rightarrow (3, 0)
   \]
   
3. For \( U(3, -4) \), the reflection will be:
   \[
   (3, -4) \rightarrow (4, -3)
   \]

Thus, the reflected vertices of the triangle \( S'T'U' \) are:

- \( S'(6, 1) \)
- \( T'(3, 0) \)
- \( U'(4, -3) \)

The reflection matches the transformation displayed on the graph.

Would you like further details, or do you have any questions?

Here are five relative questions to explore:

1. What is the general rule for reflecting over the line \( y = x \)?
2. How does reflecting over the origin affect the coordinates of a point?
3. How do you calculate the distance between two points before and after a reflection?
4. Can a reflection change the size or shape of a figure?
5. What are some real-life applications of geometric reflections?

**Tip:** When reflecting over the line \( y = -x \), always remember to switch and negate both coordinates of the original points.

Reflect the triangle STU with vertices S(-1, -6), T(0, -3), and U(3, -4) over the line y = -x.

Learn how to reflect triangle STU with vertices S(-1, -6), T(0, -3), and U(3, -4) over the line y = -x. This problem covers geometric reflections and coordinate transformations. Suitable for students in Grades 9-10.

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