Question

find the correct algebraic representation of the rotation shown below. (-y,x) (y,-x) (-x,-y) (y,x)

Explanation:

Step1: Recall rotation rules

A 90 - degree counter - clockwise rotation about the origin has the transformation rule \((x,y)\to(-y,x)\). A 90 - degree clockwise rotation about the origin has the transformation rule \((x,y)\to(y, - x)\). A 180 - degree rotation about the origin has the transformation rule \((x,y)\to(-x,-y)\).

Step2: Analyze the given rotation

By observing the pre - image \(\triangle ABC\) and the image \(\triangle A'B'C'\), we can see that it is a 90 - degree counter - clockwise rotation about the origin. For a point \((x,y)\) in the pre - image, its corresponding point in the image after a 90 - degree counter - clockwise rotation about the origin is \((-y,x)\).

Answer:

\((-y,x)\)