Question

1. use coordinate notation to describe the rotation. then determine the angle of rotation. assume the rotation is counterclockwise about the origin.

Explanation:

Step1: Recall rotation rules

For a counter - clockwise rotation about the origin, if a point $(x,y)$ is rotated 90° counter - clockwise, the new point is $(-y,x)$; if rotated 180° counter - clockwise, the new point is $(-x,-y)$; if rotated 270° counter - clockwise, the new point is $(y, - x)$. Let's take a point, say $P(-4,2)$. Its image $P'(2,4)$.

Step2: Determine the rule

If we use the general rule $(x,y)\to(-y,x)$ for a 90° counter - clockwise rotation about the origin, it matches our transformation. For example, if we have a point $(x,y)$ and its image $(-y,x)$.

Answer:

The rotation in coordinate notation is $(x,y)\to(-y,x)$ and the angle of rotation is 90°.