Question

Tentukan bayangan garis 2x+3y+8=0 yang dirotasikan 180° terhadap P(1,-2) berlawanan arah perputaran jarum jam

Answer 1

Verified answer

Rotasi [(1, -2), 180°]
x' - p = (x - p) cos 180° - (y - q) sin 180°
x' - 1 = (x - 1) (-1) - (y + 2) (0)
x' - 1 = -x + 1
x' = -x + 2
x = 2 - x'
y' - q = (x - p) sin 180° + (y - q) cos 180°
y' + 2 = (x - 1) (0) + (y + 2) (-1)
y' + 2 = -y - 2
y' = -y - 4
y = -y' - 4

persamaan garis bayangannya
2x + 3y + 8 = 0
2(2 - x') + 3(-y' - 4) + 8 = 0
4 - 2x -3y - 12 + 8 = 0
-2x - 3y = 0
2x + 3y = 0