Question

Find the x'y coordinates for the given point and the given angle of rotation, 0. Enter the exact answer or round to four decimal places, if necessary.(-13 ) 0 - 1 / 1.30 =4

Answer 1

Given:

The point is

$(x,y)=(-7.3,-\frac{2}{3})$

The angle of rotation is,

$\theta=\frac{\pi}{4}$

Required:

To find the coordinate of x'y'.

Explanation:

Now

$y^{\prime}=y\cos\theta+x\sin\theta$$=-\frac{2}{3}\cos\frac{\pi}{4}+(-7.3)\sin\frac{\pi}{4}$$\begin{gathered} =-\frac{2}{3}(0.7071)+7.3(0.7071) \\ \\ =-0.4714-5.16183 \\ \\ =-5.633 \end{gathered}$$x^{\prime}=-y\sin\theta+x\cos\theta$$\begin{gathered} =\frac{2}{3}(0.7071)-7.3(0.7071) \\ \\ =-4.69 \end{gathered}$

Final Answer:

$(x^{\prime},y^{\prime})=(-4.69,-5.633)$