Tentukan bayangan garid 3x+y = 2 karena rotasi berpusat di (1,-3) sebesar -π/2radian

jawab

garis 3x + y = 2 Rotasi {(1,-3), (-π/2)]
(a,b) = (1,-3)
α = -90°

[tex] \left[\begin{array}{ccc}x'- a\\y'-b\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] [/tex]

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

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

x' - 1 = y + 3  dan y' + 3 = 1 - x
y = x' - 1 - 3  dan x = -y' -3 +1
y = x' - 4  dan x = -y' - 2
substitusikan ke 3x + y = 2
3(-y'  - 2) + (x' - 4) = 2
-3y'  - 6 + x' - 4 = 2
x' - 3y' -10 = 2
x - 3y = 12