For a 90 degree clockwise rotation, which transformation is applied?

For a 90 degree clockwise rotation, which transformation is applied?

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

Answer: (C)

To understand why the transformation for a 90-degree clockwise rotation is represented by the equation (x, y) = (-y, x), we should consider the effect of rotating a point in the coordinate plane. When rotating a point (x, y) 90 degrees clockwise around the origin, the process involves switching the coordinates and changing the sign of the new x-coordinate. Specifically, the original x-coordinate will become the new y-coordinate, and the original y-coordinate will become the negative of the new x-coordinate. For instance: - If we take a point at (1, 0), after a 90-degree clockwise rotation, it moves to (0, -1). - The original y-coordinate (0) becomes the new x-coordinate, and the original x-coordinate (1) becomes the negative of the new y-coordinate, thus resulting in (0, -1). This transformation can be generalized using the formula (x, y) = (-y, x), effectively moving each point in the specified manner. In contrast, the other transformations do not accomplish a 90-degree clockwise rotation around the origin: - The transformation that flips the y-coordinate without altering the x-coordinate, (x, y) = (x, -y), reflects

To understand why the transformation for a 90-degree clockwise rotation is represented by the equation (x, y) = (-y, x), we should consider the effect of rotating a point in the coordinate plane.

When rotating a point (x, y) 90 degrees clockwise around the origin, the process involves switching the coordinates and changing the sign of the new x-coordinate. Specifically, the original x-coordinate will become the new y-coordinate, and the original y-coordinate will become the negative of the new x-coordinate.

For instance:

• If we take a point at (1, 0), after a 90-degree clockwise rotation, it moves to (0, -1).

• The original y-coordinate (0) becomes the new x-coordinate, and the original x-coordinate (1) becomes the negative of the new y-coordinate, thus resulting in (0, -1).

This transformation can be generalized using the formula (x, y) = (-y, x), effectively moving each point in the specified manner.

In contrast, the other transformations do not accomplish a 90-degree clockwise rotation around the origin:

• The transformation that flips the y-coordinate without altering the x-coordinate, (x, y) = (x, -y), reflects