+0

# confused

0
258
2
+282

confused

lizagame  Mar 8, 2017
#1
+88871
0

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

CPhill  Mar 8, 2017
#2
+20008
0

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':

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

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

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