https://file.aiquickdraw.com/mathbot/file/1726069681360f7go9vlu.jpg

Let's solve the problem step by step.

### Step 1: Rotation by 90° Counterclockwise
To rotate a point \((x, y)\) by 90° counterclockwise around the origin, the new coordinates \((x', y')\) are given by:
\[
(x', y') = (-y, x)
\]
We need to apply this transformation to the vertices of triangle \( \Delta ABC \).

- **Point A** is at \((-1, 2)\). After rotation:
  \[
  A' = (-2, -1)
  \]
- **Point B** is at \((1, -3)\). After rotation:
  \[
  B' = (3, 1)
  \]
- **Point C** is at \((4, 2)\). After rotation:
  \[
  C' = (-2, 4)
  \]

### Step 2: Reflection Over the Line \( y = -x \)
The reflection of a point \((x, y)\) over the line \( y = -x \) is given by swapping and negating the coordinates:
\[
(x', y') = (-y, -x)
\]
Now, apply this transformation to the new vertices \(A', B', C'\).

- **Point A'** is at \((-2, -1)\). After reflection:
  \[
  A'' = (1, 2)
  \]
- **Point B'** is at \((3, 1)\). After reflection:
  \[
  B'' = (-1, -3)
  \]
- **Point C'** is at \((-2, 4)\). After reflection:
  \[
  C'' = (-4, 2)
  \]

### Final Coordinates of the Transformed Triangle
The new vertices of the transformed triangle are:
- \( A'' = (1, 2) \)
- \( B'' = (-1, -3) \)
- \( C'' = (-4, 2) \)

By checking these points on the coordinate plane, the transformed triangle can be graphed.

Would you like to see further details or explanations? 

Here are five questions to expand your understanding:
1. How would the transformation change if the triangle was rotated by 180° instead of 90°?
2. What happens when you reflect a shape over the line \(y = x\) instead of \(y = -x\)?
3. How would the transformation rules change if you reflected over the x-axis?
4. What would happen if the rotation was clockwise instead of counterclockwise?
5. Can you describe the combined transformation as a single matrix operation?

**Tip:** Remember that combining transformations (like rotation and reflection) can often be simplified by using matrices, which makes it easier to apply multiple transformations at once.

The figure shows triangle ABC plotted on a coordinate plane. The triangle is first rotated by 90° counterclockwise about the origin and then reflected about the line y = -x. Which graph shows the transformed triangle?

Learn how to transform triangle ABC by rotating 90° counterclockwise and reflecting over the line y = -x. This detailed guide covers key geometric transformations and step-by-step calculations for Grades 8-10.

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