Question

question 3
question
write a function to represent the point (x,y) rotated 90° counterclockwise about the origin.
r(x,y) =

Explanation:

Step1: Recall rotation matrix

The rotation matrix for a \(90^{\circ}\) counter - clockwise rotation about the origin is \(

$$\begin{bmatrix}0&-1\\1&0\end{bmatrix}$$

\).

Step2: Apply matrix - vector multiplication

If we have a point \((x,y)\) represented as the vector \(

$$\begin{bmatrix}x\\y\end{bmatrix}$$

\), then \(

$$\begin{bmatrix}0&-1\\1&0\end{bmatrix}$$

$$\begin{bmatrix}x\\y\end{bmatrix}$$

=

$$\begin{bmatrix}0\times x+(-1)\times y\\1\times x + 0\times y\end{bmatrix}$$

\).

Answer:

\(R(x,y)=(-y,x)\)