Question

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 counter - clockwise rotation about the origin 90 degrees clockwise rotation about the origin 180 degrees (y,x) (x, - y) (y, - x)

Explanation:

Step1: Recall 90 - degree counter - clockwise rotation rule

For a 90 - degree counter - clockwise rotation about the origin of a point \((x,y)\), the new coordinates are \((-y,x)\).

Step2: Recall 90 - degree clockwise rotation rule

For a 90 - degree clockwise rotation about the origin of a point \((x,y)\), the new coordinates are \((y, - x)\).

Step3: Recall 180 - degree rotation rule

For a 180 - degree rotation about the origin of a point \((x,y)\), the new coordinates are \((-x,-y)\).

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: \((-x,-y)\)