Answer :
To determine which transformation produces the specified image, we need to systematically apply each proposed transformation to the original vertices and see if we get the desired transformed vertices.
Step 1: Applying the first transformation [tex]$(x, y) \rightarrow (x, -y)$[/tex]
- For vertex \( A(-2, -2) \):
[tex]\[ (-2, -2) \rightarrow (-2, -(-2)) = (-2, 2) \][/tex]
- For vertex \( B(-1, 1) \):
[tex]\[ (-1, 1) \rightarrow (-1, -(1)) = (-1, -1) \][/tex]
- For vertex \( C(3, 2) \):
[tex]\[ (3, 2) \rightarrow (3, -(2)) = (3, -2) \][/tex]
Transformation [tex]$(x, y) \rightarrow (x, -y)$[/tex] results in the vertices: \(A^{\prime}(-2, 2)\), \(B^{\prime}(-1, -1)\), \(C^{\prime}(3, -2)\), which matches the given image vertices.
Conclusion:
The transformation \( (x, y) \rightarrow (x, -y) \) is the required transformation.
Therefore, the correct transformation that produces the given image is:
[tex]\[ \boxed{(x, y) \rightarrow (x, -y)} \][/tex]
Step 1: Applying the first transformation [tex]$(x, y) \rightarrow (x, -y)$[/tex]
- For vertex \( A(-2, -2) \):
[tex]\[ (-2, -2) \rightarrow (-2, -(-2)) = (-2, 2) \][/tex]
- For vertex \( B(-1, 1) \):
[tex]\[ (-1, 1) \rightarrow (-1, -(1)) = (-1, -1) \][/tex]
- For vertex \( C(3, 2) \):
[tex]\[ (3, 2) \rightarrow (3, -(2)) = (3, -2) \][/tex]
Transformation [tex]$(x, y) \rightarrow (x, -y)$[/tex] results in the vertices: \(A^{\prime}(-2, 2)\), \(B^{\prime}(-1, -1)\), \(C^{\prime}(3, -2)\), which matches the given image vertices.
Conclusion:
The transformation \( (x, y) \rightarrow (x, -y) \) is the required transformation.
Therefore, the correct transformation that produces the given image is:
[tex]\[ \boxed{(x, y) \rightarrow (x, -y)} \][/tex]
