https://file.aiquickdraw.com/mathbot/file/17261741635296kn74dow.jpg

To reflect the triangle \( \Delta RST \) over the line \( y = -x \), we need to apply the following transformation to the coordinates of each point in the triangle:

- For any point \( (x, y) \), after reflecting over the line \( y = -x \), the new coordinates become \( (-y, -x) \).

Let's calculate the reflected points:

- \( R \) is at \( (-4, -4) \), so after reflecting over \( y = -x \), the new coordinates of \( R' \) will be \( (4, 4) \).
- \( S \) is at \( (2, -4) \), so after reflecting over \( y = -x \), the new coordinates of \( S' \) will be \( (4, -2) \).
- \( T \) is at \( (-4, -6) \), so after reflecting over \( y = -x \), the new coordinates of \( T' \) will be \( (6, 4) \).

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

Do you want to see a detailed breakdown of these steps or have any questions on how the reflection works?

Here are 5 related questions for further understanding:
1. What is the rule for reflecting a point over the line \( y = x \)?
2. How do you find the equation of a line given two points?
3. What is the relationship between a line and its perpendicular bisector?
4. How can reflections be applied in solving real-world geometry problems?
5. How do you graph a line with a negative slope?

**Tip**: When reflecting over \( y = -x \), simply swap and negate the coordinates of the points to get the reflected image!

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

Learn how to reflect triangle ΔRST over the line y = -x by applying coordinate transformations. This problem involves understanding reflection rules and geometric properties in coordinate geometry. Suitable for students in Grades 8-10.

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