persamaan bayangan garis y=2x+12 oleh rotasi pada pusat (2,1) dengan sudut rotasi 90 derajat adalah...

jawab
y= 2x + 12
P(a,b) = (2,1)
α = 90°

[tex] \left[\begin{array}{ccc}x'\\y'\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]\,+ \left[\begin{array}{ccc}a\\b\end{array}\right] [/tex]


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


x' = - y + 3 → y = 3 - x'
y' = x -1 → x = y' + 1
substitusikan ke y = 2x + 12

3- x' = 2(y' + 1) + 12
3  - x' = 2y' + 2 + 12
3 - x = 2y + 14
2y = -x + 3 - 14
2y = -  x - 11
x + 2y + 11= 0