[tex]\begin{gathered} x^{\prime}=x\cos \theta+y\sin (\theta) \\ y^{\prime}=-x\sin (\theta)+\cos (\theta) \end{gathered}[/tex]
This is a rotation of 180 clockwise, so:
[tex]\begin{gathered} x^{\prime}=x\cos (180)+y\sin (180) \\ y^{\prime}=-x\sin (180)+y\cos (180) \\ x^{\prime}=-x \\ y^{\prime}=-y \\ \text{The rule is:} \\ (x,y)\to(-x,-y) \\ \text{Verify:} \\ \text{for example:} \\ E=(-1,3) \\ E^{\prime}=(1,-3) \\ (-1,3)\to(-x,-y)\to(1,-3) \end{gathered}[/tex]
