Question

2 matching 2 points match the coordinates of the original point (x,y) with the coordinates of each rotated point in terms of x and y. rotation about the origin 90 degrees counterclockwise (y,-x) rotation about the origin 90 degrees clockwise (-y,x) rotation about the origin 180 degrees (-x,-y)

Explanation:

Step1: Recall rotation rules

For a 90 - degree counter - clockwise rotation about the origin, we use the transformation rule $(x,y)\to(-y,x)$. But the correct rule for 90 - degree counter - clockwise rotation of a point $(x,y)$ about the origin is $(x,y)\to(-y,x)$. For 90 - degree clockwise rotation, we swap $x$ and $y$ and change the sign of the new $y$, so $(x,y)\to(y, - x)$. For 180 - degree rotation about the origin, we change the sign of both coordinates, so $(x,y)\to(-x,-y)$.

Answer:

Rotation about the origin 90 degrees counterclockwise: $(-y,x)$
Rotation about the origin 90 degrees clockwise: $(y, - x)$
Rotation about the origin 180 degrees: $(-x,-y)$