Tentukan bayangan garid 3x+y = 2 karena rotasi berpusat di (1,-3) sebesar -π/2radian

Tentukan bayangan garid 3x+y = 2 karena rotasi berpusat di (1,-3) sebesar -π/2radian

Jawaban Terkonfirmasi

Jawab

garis 3x + y = 2 Rotasi {(1,-3), (-π/2)]
(a,b) = (1,-3)
α = -90°

$left[begin{array}{ccc}x'- a\y'-bend{array}right],=, left[begin{array}{ccc}cos,(-90)&-sin(-90)\sin(-90)&cos(90)end{array}right] left[begin{array}{ccc}x-a\y-bend{array}right]$

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

$left[begin{array}{ccc}x'-1\y'+3end{array}right],=,left[begin{array}{ccc}y+3\1- xend{array}right]$

x' – 1 = y + 3 dan y' + 3 = 1 – x
y = x' – 1 – 3 dan x = -y' -3 +1
y = x' – 4 dan x = -y' – 2
substitusikan ke 3x + y = 2
3(-y' – 2) + (x' – 4) = 2
-3y' – 6 + x' – 4 = 2
x' – 3y' -10 = 2
x – 3y = 12