Question

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

Explanation:

Step1: Recall rotation rules

For a clock - wise rotation about the origin, the general rule for a 90 - degree rotation of a point $(x,y)$ is $(x,y)\to(y, - x)$, for 180 - degree rotation is $(x,y)\to(-x,-y)$ and for 270 - degree rotation is $(x,y)\to(-y,x)$.

Step2: Identify key points

Let's take a point, say $D(- 3,-2)$. Its image $D'(1, - 3)$.

Step3: Determine rotation rule

If we assume a 90 - degree clock - wise rotation of a point $(x,y)$ to $(y,-x)$. Let's check with point $D(-3,-2)$. After 90 - degree clock - wise rotation, $x=-3,y = - 2$, and the new point is $(-2,3)$ which is wrong. For 180 - degree clock - wise rotation of $(x,y)=(-3,-2)$ gives $(3,2)$ which is wrong. For 270 - degree clock - wise rotation of $(x,y)=(-3,-2)$ where $x=-3,y=-2$, the new point is $(2,-3)$ which is wrong.
Let's use vectors or the fact that if we consider the orientation of the figure. If we take two adjacent sides of the original figure and their corresponding sides in the rotated figure. We know that for a 90 - degree clock - wise rotation of a point $(x,y)$ about the origin, the coordinate notation is $(x,y)\to(y,-x)$.
Let's assume a general point $(x,y)$ on the original figure. After rotation, we can observe from the figure that the rotation rule is $(x,y)\to(y,-x)$.

Step4: Determine angle of rotation

Since the rotation rule is $(x,y)\to(y,-x)$, the angle of clock - wise rotation about the origin is 90 degrees.

Answer:

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