bayangan titik p (1,1) jika diputar dengan titik pusat a (3,4) dan sudut putar 90 derajat adalah

jawab
P(x,y)= (1,1)  → x = 1, y = 1
A(a,b)= (3,4) → a = 3 , b = 4
α = 90

[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}1-3\\1-4\end{array}\right]\,+ \left[\begin{array}{ccc}1\\4\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}-2\\-3\end{array}\right]\,+ \left[\begin{array}{ccc}1\\4\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}x'\\y'\end{array}\right]\,=\, \left[\begin{array}{ccc}3\\-2\end{array}\right]\,+ \left[\begin{array}{ccc}1\\4\end{array}\right]\,=\, \left[\begin{array}{ccc}4\\2\end{array}\right] [/tex]