Tentukan bayangan p (3,-5) jika dirotasi 90 dengan pusat rotasi A(1,2) kemudian buat gambarnya

jawab

P(x,y) = (3, - 5)
R {(A, 90} 
A(a,b)= (1,2)

[tex] \left[\begin{array}{ccc}x'\\y'\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]\,+\, \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}x-1\\y-2\end{array}\right]\,+\, \left[\begin{array}{ccc}1\\2\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}3-1\\-5-2\end{array}\right]\,+\, \left[\begin{array}{ccc}1\\2\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}x'\\y'\end{array}\right]\,=\, \left[\begin{array}{ccc}(7+1)\\(2+2)\end{array}\right][/tex]

P' (x', y') = (8, 4)