bayangan titik (4, -5) rotasi R(P, 90) adalah (10,5). titik pusat rotasi tersebut adalah jawab beserta caranya

jawab
A(x,y) = (4,- 5)
A'(x',y') = (10, 5)
P(a,b)
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\\y\end{array}\right] [/tex]

[tex] \left[\begin{array}{ccc}10-a\\5-b\end{array}\right]\,= \left[\begin{array}{ccc}0&-1\\1&0\end{array}\right]\left[\begin{array}{ccc}4\\5\end{array}\right] [/tex]


[tex]\left[\begin{array}{ccc}10-a\\5-b\end{array}\right]\,= \left[\begin{array}{ccc}5\\4\end{array}\right][/tex]

10 - a = 5 → a = 5
5 - b = 4 → b  = 1

Pusat rotasi (a,b) = (5, 1)