What is the result of rotating a point (x, y) by 270 degrees or -90 degrees?

What is the result of rotating a point (x, y) by 270 degrees or -90 degrees?

• A. (y, -x)
• B. (-y, x)
• C. (x, y)
• D. (-x, -y)

Answer: (A)

The rotation of a point in the coordinate plane can be determined by applying rotation rules depending on the angle of rotation. When rotating a point (x, y) by 270 degrees counterclockwise or equivalently -90 degrees clockwise, the position of the point in relation to the origin shifts accordingly. In the case of a 270-degree counterclockwise rotation, the new coordinates can be derived through the transformation: - The x-coordinate of the original point becomes the negative of the y-coordinate, and - The y-coordinate becomes the x-coordinate. So, if we take the point (x, y) and rotate it 270 degrees, the transformation results in the coordinates switching places with one being negated. Therefore, the coordinates of the point after this rotation will be (y, -x). This transformation is crucial in understanding how points move within the Cartesian plane based on angle measurements, showing the relationships between original coordinates and their new positions after rotation.

The rotation of a point in the coordinate plane can be determined by applying rotation rules depending on the angle of rotation. When rotating a point (x, y) by 270 degrees counterclockwise or equivalently -90 degrees clockwise, the position of the point in relation to the origin shifts accordingly.

In the case of a 270-degree counterclockwise rotation, the new coordinates can be derived through the transformation:

• The x-coordinate of the original point becomes the negative of the y-coordinate, and

• The y-coordinate becomes the x-coordinate.

So, if we take the point (x, y) and rotate it 270 degrees, the transformation results in the coordinates switching places with one being negated. Therefore, the coordinates of the point after this rotation will be (y, -x).

This transformation is crucial in understanding how points move within the Cartesian plane based on angle measurements, showing the relationships between original coordinates and their new positions after rotation.