Tentukan bayangan titik B (3,-1) karena rotasi dengan pusat (2,1) dan sudut putar (- 90 °)

jawab

B(x,y)= (3,-1)
P(a,b) = (2,1)
x= -90°

[tex] \left[\begin{array}{ccc}x'\\y'\end{array}\right]\,=\, \left[\begin{array}{ccc}cos\,(-90)&-sin\,(-90)\\sin\,(-90)&cos\,(-90)\end{array}\right]\, \left[\begin{array}{ccc}x-a\\y-b\end{array}\right]\,+\, \left[\begin{array}{ccc}a\\b\end{array}\right] [/tex]

[tex] \left[\begin{array}{ccc}x'\\y'\end{array}\right]\,=\, \left[\begin{array}{ccc}0&1\\-1&0\end{array}\right]\, \left[\begin{array}{ccc}3-2\\-1-1\end{array}\right]\,+\, \left[\begin{array}{ccc}2\\1\end{array}\right] [/tex]


[tex] \left[\begin{array}{ccc}x'\\y'\end{array}\right]\,=\, \left[\begin{array}{ccc}0&1\\-1&0\end{array}\right]\, \left[\begin{array}{ccc}1\\-2\end{array}\right]\,+\, \left[\begin{array}{ccc}2\\1\end{array}\right] [/tex]

[tex]\left[\begin{array}{ccc}x'\\y'\end{array}\right]\,=\, \left[\begin{array}{ccc}-2\\-1\end{array}\right]\,+\, \left[\begin{array}{ccc}2\\1\end{array}\right] [/tex]

x' = 0
y' = 0
B' (x' , y') = ( 0 , 0)