To determine the coordinates of polygon \( A'B'C'D' \) after a 90° counterclockwise rotation of polygon \( ABCD \), we can apply the rotation transformation to each vertex of the original polygon.
The vertices of polygon \( ABCD \) are:
- \( A(0, 0) \)
- \( B(5, 2) \)
- \( C(5, -5) \)
- \( D(0, -3) \)
The formula for rotating a point \( (x, y) \) 90° counterclockwise about the origin is: \[ (x', y') = (-y, x) \]
Applying this transformation to each vertex:
-
For \( A(0, 0) \): \[ A'(0, 0) \rightarrow A'(0, 0) \]
-
For \( B(5, 2) \): \[ B'(5, 2) \rightarrow B'(-2, 5) \]
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For \( C(5, -5) \): \[ C'(5, -5) \rightarrow C'(5, 5) \]
-
For \( D(0, -3) \): \[ D'(0, -3) \rightarrow D'(3, 0) \]
Thus, the coordinates of the rotated polygon \( A'B'C'D' \) are:
- \( A'(0, 0) \)
- \( B'(-2, 5) \)
- \( C'(5, 5) \)
- \( D'(3, 0) \)
Comparing these results with the provided options:
- The first option is \( A'(0, 0), B'(-2, 5), C'(5, 5), D'(3, 0) \), which matches our calculation.
So, the correct answer is: A′(0, 0), B′(−2, 5), C′(5, 5), D′(3, 0)