Garis y = x + 1 dirotasikan terhadap pusat o(0,0) sebesar 90° berlawanan arah jarum jam. Persamaan bayangannya adalah

jawab

(x,y) --> Rotasi [O, 90]  --> (x' , y')

x' =  - y  atau  y = - x'
y' =  x  atau x =  y'
subs  ke garis y = x + 1 --> - x' = y' + 1
x ' = - y' - 1
atau
x = -y - 1 
atau
y = -x - 1

pake matriks

[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\\y\end{array}\right] [/tex]

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

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

x' =  - y  atau  y = - x'
y' =  x  atau x =  y'
subs  ke garis y = x + 1 --> - x' = y' + 1
x ' = - y' - 1
atau
x = -y - 1 
atau
y = -x - 1