confused

The x, y coordinates of F'  =

 [1cos(180) - 5sin(180),  1sin(180) + 5cos(180) ]  =   [ -1 , - 5 ]

And the x , y coordinates of G'  =

 [4cos(180) - (-3)sin(180),  4sin(180) + (-3)cos(180) ]  =   [ -4 , 3 ]

"b" is correct

confused

Matrix Rotation counterclockwise:

$\begin{array}{|rcll|} \hline \begin{pmatrix} \cos(\varphi) & \sin (\varphi) \\ -\sin(\varphi) & \cos (\varphi) \\ \end{pmatrix} \stackrel{\varphi=180^{\circ}} \rightarrow \begin{pmatrix} -1 & 0 \\ 0 & -1 \\ \end{pmatrix} \\ \hline \end{array}$

The point P becomes to P':

$\begin{array}{|rcll|} \hline \binom{x}{y}\cdot \begin{pmatrix} -1 & 0 \\ 0 & -1 \\ \end{pmatrix} = \binom{-x}{-y} \\ \hline \end{array}$

$\text{Let}\ F =\binom{1}{5} \\ \text{Let}\ G =\binom{4}{-3}$

$\begin{array}{|rcll|} \hline F'=\binom{1}{5}\cdot \begin{pmatrix} -1 & 0 \\ 0 & -1 \\ \end{pmatrix} = \binom{-1}{-5} \\ G'=\binom{4}{-3}\cdot \begin{pmatrix} -1 & 0 \\ 0 & -1 \\ \end{pmatrix} = \binom{-4}{3} \\ \hline \end{array}$

The answer is b.