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confused

lizagame  Mar 8, 2017
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 #1
avatar+79794 
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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

 

 

cool cool cool

CPhill  Mar 8, 2017
 #2
avatar+18777 
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':

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

 

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

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

 

The answer is b.

 

laugh

heureka  Mar 9, 2017

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