To determine which transformation produces the given result, let us analyze how the original vertices are transformed to the new vertices:

Original Vertices and Transformed Vertices:

1. A (−2, −2) → A′ (2, −2)
2. B (−1, 1) → B′ (1, 1)
3. C (3, 2) → C′ (−3, 2)

Testing the Transformations:

Option 1: $(x, y) → (x, −y)$

• A(−2, −2) → (−2, 2) → Incorrect.
• This does not match the transformation.

Option 2: $(x, y) → (−y, x)$

• A(−2, −2) → (2, −2) → Matches!
• B(−1, 1) → (−1, 1) → Matches!
• C(3, 2) → (−3, 2) → Matches!
• This transformation is consistent with all vertices.

Option 3: $(x, y) → (−x, y)$

• A(−2, −2) → (2, −2) → Incorrect.
• This does not match the transformation.

Option 4: $(x, y) → (y, −x)$

• A(−2, −2) → (−2, 2) → Incorrect.
• This does not match the transformation.

Correct Answer:

The transformation that produces the given image is: $(x, y) → (−y, x)$.

Would you like further details or additional examples to explore this concept?

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Related Questions:

1. How do you verify transformations using matrix representation?
2. What is the geometric meaning of $(−y, x)$ in terms of rotation?
3. How do transformations affect the area of a triangle?
4. How can you identify a transformation when given a specific shape or figure?
5. What are other common transformations involving reflections and rotations?

Tip: To analyze transformations effectively, always test one vertex at a time systematically.