tentukan bayangan titik (-3,1) oleh rotasi sudut 90° dengan koordinat titik pusat (-2,3)!

jawab

(x,y)= (-3,1)
α = 90
pusat rotasi (a,b)= (-2,3)
a= -2
b = 3

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

Rotasi

(x') = (0 - 1)  (-3 + 2) +  (-2) = (0 - 1)  (-1) + (-2) =  (2) +  (-2) = (0)
(y')    (1   0)  (1  -  3)      (3)    (1    0)  (-2)    (3)     (-1)     (3)     (2)

Jadi, bayangannya adalah (0, 2)

Semoga Membantu!!!