A pre-image point is rotated 90° clockwise. If the pre-image point had the coordinates (3, -5), what are the coordinates of its image point

Question

hero · Answer

Much easier to find with graph paper.

anonymous · Answer

$$ \Large \left(\begin{matrix}x' \ y'\end{matrix}\right)=\left(\begin{matrix}\cos \alpha & - \sin \alpha \ \sin \alpha & \cos \alpha\end{matrix}\right)\left(\begin{matrix}x \ y\end{matrix}\right)$$

anonymous · Answer

not sure if you know how to apply that already, however that's for a matrix projection

hero · Answer

You do not need to use that to solve this problem.

anonymous · Answer

For rotation around the origin with $\alpha = 90^\circ $ the points just become normal to each other, so components exchange and signs flip for one, in this case
(-5/3)