bayangan garis 3x-2y+4=0 oleh refleksi terhadap garis y=x dilanjutkan oleh rotasi dengan pusat O(0,0) sejauh setengah putaran adalah

jawab

T1 = Refleksi y = x  = [tex] \left[\begin{array}{ccc}0&1\\1&0\end{array}\right] [/tex]

T2 = Rotasi [O, 90] = [tex]\left[\begin{array}{ccc}0&-1\\1&0\end{array}\right] [/tex]


Transformasi  T1 dilanjutkan T2 → (x', y' ) = T2 o T1  (x, y)

[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}0&1\\1&0\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right][/tex]

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

[tex]\left[\begin{array}{ccc}x'\\y'\end{array}\right]\,=\,\left[\begin{array}{ccc}-x\\y\end{array}\right] \\ \\ \\ x= - x'\, dan\,\, y = y' subs\, ke\,\, 3x - 2y+ 4= 0[/tex]


3(-x') - 2(y') + 4 = 0
- 3x - 2y + 4 = 0
atau
3x + 2y - 4 = 0