PLEASE HELP THANKS!!!

$(2,3)$  is at the polar coordinates of  $(r,\theta)$  so:

$2\ =\ r\cos\theta\\~\\ 3\ =\ r\sin\theta$

$(x_1,y_1)$  is at the polar coordinates of  $(2r,\theta+\frac{\pi}{2})$  so:

$\begin{array}{} x_1\ =\ (2r)\cos(\theta+\frac{\pi}{2})&=&(2r)(-\sin\theta)&=&(-2)(r\sin\theta)&=&(-2)(3)&=&-6\\~\\ y_1\ =\ (2r)\sin(\theta+\frac{\pi}{2})&=&(2r)(\cos\theta)&=&(2)(r\cos\theta)&=&(2)(2)&=&4 \end{array}$

$(x_2,y_2)$  is at the polar coordinates of  $(-r,-\theta)$  so:

$\begin{array}{c} x_2\ =\ (-r)\cos(-\theta)&=&(-r)\cos\theta&=&-(r\cos\theta)&=&-2\\~\\ y_2\ =\ (-r)\sin(-\theta)&=&(-r)(-\sin\theta)&=&r\sin\theta&=&3 \end{array}$_