Describe the transformation in the diagram. (1 point) Responses 90° counterclockwise rotation about the origin 90 degrees counterclockwise rotation about the origin 90° clockwise rotation about the origin 90 degrees clockwise rotation about the origin 270° counterclockwise rotation about the origin 270 degrees counterclockwise rotation about the origin 180° counterclockwise rotation about the origin
The transformation in the diagram is a 90° counterclockwise rotation about the origin.
The transformation in the diagram described is a 90° counterclockwise rotation about the origin.
To determine the correct description of the transformation in the diagram, we need to understand what a rotation around the origin means. In a coordinate plane, the origin is the point (0,0), which is where the x-axis and y-axis intersect.
A 90° counterclockwise rotation about the origin means that every point on the diagram will rotate 90° in a counterclockwise direction around the origin. This means that if a point was initially at coordinates (x, y), it will now be at coordinates (-y, x). In other words, the x-coordinate becomes the negative of the original y-coordinate, and the y-coordinate becomes the original x-coordinate.
Similarly, a 90° clockwise rotation about the origin means that every point on the diagram will rotate 90° in a clockwise direction around the origin. This means that if a point was initially at coordinates (x, y), it will now be at coordinates (y, -x). In this case, the original x-coordinate becomes the new y-coordinate, and the original y-coordinate becomes the negative of the new x-coordinate.
A 270° counterclockwise rotation about the origin means that every point on the diagram will rotate 270° in a counterclockwise direction around the origin. This is equivalent to rotating 90° clockwise. Therefore, the coordinates of each point will follow the same transformation as described above for a 90° clockwise rotation.
Similarly, a 270° clockwise rotation about the origin means that every point on the diagram will rotate 270° in a clockwise direction around the origin. This is equivalent to rotating 90° counterclockwise. Therefore, the coordinates of each point will follow the same transformation as described above for a 90° counterclockwise rotation.
Finally, a 180° counterclockwise rotation about the origin means that every point on the diagram will rotate 180° in a counterclockwise direction around the origin. This means that the x-coordinate becomes the negative of the original x-coordinate, and the y-coordinate becomes the negative of the original y-coordinate.
Based on the description of the transformations provided, the correct answer for the transformation in the diagram is a 90° counterclockwise rotation about the origin.