Answer:
- A 90° counterclockwise rotation about the origin and then a 180° rotation about the origin. → A 90° clockwise rotation about the origin.
- A reflection across the x-axis and then a reflection across the y-axis. → A 180° rotation about the origin.
- A 90° clockwise rotation about the origin and then a rotation 180° about the origin. → A 90° counterclockwise rotation about the origin.
Step-by-step explanation:
A 90° counterclockwise rotation about the origin followed by a 180° rotation about the origin results in a net rotation of 270° counterclockwise about the origin. This is equivalent to a 90° clockwise rotation if we consider the full 360° rotation.
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A reflection across the x-axis and then a reflection across the y-axis is equivalent to a 180° rotation about the origin.
When a point is reflected across the x-axis, the x-coordinate is unchanged, but the y-coordinate is negated. Similarly, when a point is reflected across the y-axis, the y-coordinate is unchanged but the x-coordinate is negated. Therefore, a reflection across the x-axis followed by a reflection across the y-axis results in the negating of the x and y coordinates.
A 180° rotation about the origin is a transformation in which each point in a plane is rotated by 180° counterclockwise or clockwise around the origin, resulting in the negating of the x and y coordinates.
[tex]\dotfill[/tex]
A 90° clockwise rotation about the origin followed by a 180° rotation about the origin results in a net rotation of 270° clockwise about the origin. This is equivalent to a 90° counterclockwise rotation if we consider the full 360° rotation.
