Chapter 10.4, Problem 63PE

Recall from Section 9.3 that a point $P\left(x,y\right)$ can be represented by the matrix $\left[\begin{array}{c}x\\ y\end{array}\right]$ . By applying matrix addition, subtraction, or multiplication we can translate the point or rotate the point to a new location. Given $P\left(x,y\right)$ , the product $\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]$ gives the coordinates of the point rotated by an angle $\theta$ about the origin.

a. Write a product of matrices that rotates the point $\left(6,2\right)$ counterclockwise $60°$ about the origin.

b. Compute the product in part (a).

c. Graph the point $\left(6,2\right)$ and the point found in part (b) to illustrate the rotation.Round the coordinates of the rotated point to $1$ decimal place.