suatu lingkaran persamaan (x-2)^2 + (y+1)^2=9 direfleksi thdp garis y=-x kemudian didilatasi dengan skala 3 dan berpusat pda (0.0) tentuian persamaan lingkaran

jawab

(x-2)² + (y+1)²  = 9

T1 → R garis y = - x
T2 → D[0, 3]

T2 o T1 (x,y) = (x', y')

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

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

x'= - 3y → y = -1/3 x'
y'= - 3x → x = - 1/3 y'
substitusi ke (x - 2)² + (y+1)² = 9
(- 1/3 y - 2)² + (-1/3 x + 1)² = 9
1/9 y² + 4/3 y + 4 + 1/9 x² - 2/3 x + 1 = 9
1/9 y² + 1/9 x² + 4/3 y - 2/3 x - 4 = 0....}kali 9
x² + y² - 6x + 12y - 36= 0