Persamaan bayangan kurva y=x*2 - 3x + 1, karena rotasi pusat O sebesar 180 derajat dilanjutkan refleksi terhadap garis y = -x adalah?

Transformasi Geometri
Kelas XII

Matriks yg bersesuaian dengan rotasi pusat O sebesar 180° :
[tex] T_1 = \left(\begin{array}{cc}\cos 180 & - \sin 180\\ \sin 180 & \cos 180 \end{array}\right) \\
= \left(\begin{array}{cc}-1 & 0 \\ 0 & -1\end{array}\right) [/tex]

Matriks yang bersesuaian dengan refleksi garis y = -x
[tex] T_2 = \left(\begin{array}{cc} 0 & -1 \\ -1 & 0 \end{array}\right) [/tex]

[tex] M = \left(\begin{array}{cc} 0 & -1 \\ -1 & 0 \end{array}\right) \left(\begin{array}{cc} -1 & 0 \\ 0 & -1 \end{array}\right) \\
M = \left(\begin{array}{cc} 0 & 1 \\ 1 & 0 \end{array}\right) [/tex]

[tex] \left(\begin{array}{cc} x \\ y \end{array}\right) = \left(\begin{array}{cc} 0 & 1 \\ 1 & 0 \end{array}\right)^{-1} \left(\begin{array}{cc} x' \\ y' \end{array}\right) \\
\left(\begin{array}{cc} x \\ y \end{array}\right) = \frac{1}{-1} \left(\begin{array}{cc} 0 & -1 \\ -1 & 0 \end{array}\right) \left(\begin{array}{cc} x' \\ y' \end{array}\right) \\
\left(\begin{array}{cc} x \\ y \end{array}\right) = \left(\begin{array}{cc} 0 & 1 \\ 1 & 0 \end{array}\right) \left(\begin{array}{cc} x' \\ y' \end{array}\right) \\
\left(\begin{array}{cc} x \\ y \end{array}\right) = \left(\begin{array}{cc} y' \\ x' \end{array}\right) [/tex]

Didapat
x = y'
y = x'

Subtitusikan ke pers. awal
y = x² - 3x + 1
x' = (y')² - 3y' + 1
x = y² - 3y + 1