Titik (4,2) dirotasikan sebesar 90° dengan pusat P(1,2) akan berpindah ke posisi titik dengan koordinat...

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jawab

Titik (x,y) = (4,2) → x= 4, y = 2
R[(a,b), α) = R[ (1,2) , 90°)→ a = 1, b = 2, 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- a\\y-b\end{array}\right] [/tex]

[tex]\left[\begin{array}{ccc}x'- 1\\y'-2\end{array}\right]\,= \left[\begin{array}{ccc}0&-1\\1&0\end{array}\right] \left[\begin{array}{ccc}4- 1\\2-2\end{array}\right] [/tex]

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

x' - 1 = 0 →  x' = 1

y' - 2 = 3  → y' = 5

(x' , y' ) = (1 , 5)