Given a point on a geometric figure (x, y),what is the new figure is rotated clockwise about the origin 270 degrees?
If we rotate a point (x, y) about the origin by 270 degrees clockwise, the coordinates of the new point will be (y, -x).
This can be explained as follows:
- A 90-degree clockwise rotation about the origin can be achieved by swapping the x and y coordinates and changing the sign of the new x coordinate. The new coordinates become (y, -x).
- Another 90-degree clockwise rotation can be achieved by again swapping the x and y coordinates and changing the sign of the new x coordinate. The new coordinates become (-y, x).
- Finally, applying a 90-degree clockwise rotation again results in swapping the x and y coordinates and changing the sign of the new x coordinate. The new coordinates become (-x, -y).
Therefore, rotating a point (x, y) about the origin by 270 degrees clockwise yields the new coordinates (-y, x).