1. Persamaan bayangan garis y = 2x - 3 karena refleksi terhadap garis y = -x dilanjutkan refleksi terhadap y = x adalah.... 2. Bayangan kurva y = x + 1 jika dit

jawab

(1) T1 = refleksi y = - x
T2 = refleksi y = x
T2oT1 (x,y) = (x',y')
[tex]\left[\begin{array}{ccc}0&1\\1&0\end{array}\right] \left[\begin{array}{ccc}0&-1\\-1&0\end{array}\right] \, \left[\begin{array}{ccc}x\\y\end{array}\right]\,= \left[\begin{array}{ccc}x'\\y'\end{array}\right]\,\\ \\ x\, = x' dan \, y= -y'\\ y = 2x-3 \, banyangan nya -y' = 2(-x') - 3 \, atau\, y = 2x +3 [/tex]


(2)
T1= transformasi matriks
T2 = refleksi sumbu x
T2oT1 (x,y)= (x',y')

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

x + 2y = x'
-y = y' ..}kali 2
x + 2y = x'
-2y = 2y'...(+)
x = x'  + 2y'
dan y = -y'

y =  x + 1
-y' = x' + 2y'  +1
-y'  - 2y' =  x' + 1
-3y' = x' + 1
atau
x + 3y +1 = 0