To describe the transformations listed involving rotations about the origin, let's break down what each rotation does to a point (x, y) in the coordinate plane.
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90° Counterclockwise Rotation about the Origin:
- A point (x, y) transforms to (-y, x). This means the point moves to the left of the y-axis and then up around the origin.
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180° Counterclockwise Rotation about the Origin:
- A point (x, y) transforms to (-x, -y). This transformation flips the point over the origin, moving it to the opposite quadrant.
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90° Clockwise Rotation about the Origin:
- A point (x, y) transforms to (y, -x). This is the reverse of the 90° counterclockwise rotation, moving the point to the right of the y-axis and then down around the origin.
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270° Counterclockwise Rotation about the Origin:
- A point (x, y) transforms to (y, -x). This is equivalent to a 90° clockwise rotation, effectively moving the point in the same manner as described above.
So, the transformations alter the coordinates of a point (x, y) based on the degree and direction of the rotation around the origin.