Question

3.3 rotations
assignment
geometry rotations explained (90, 180, 270, 360)
what is a 360 degree rotation of (x, y)?
open - ended question
type your answer here

Explanation:

Step1: Recall rotation rule

A 360 - degree rotation about the origin in a coordinate - plane is equivalent to no rotation. The general rule for a rotation of a point $(x,y)$ about the origin by an angle $\theta$ is given by the rotation matrix. For $\theta = 360^{\circ}$, using the rotation matrix

$$\begin{bmatrix}\cos\theta&-\sin\theta\\\sin\theta&\cos\theta\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}$$

. Since $\cos(360^{\circ}) = 1$ and $\sin(360^{\circ})=0$, we have

$$\begin{bmatrix}1&0\\0&1\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}x\\y\end{bmatrix}$$

.

Answer:

The 360 - degree rotation of the point $(x,y)$ is the point $(x,y)$ itself.