Persamaan bayangan garis x-y+1=0 oleh rotasi terhadap O(0,0) sebesar v/2 radian adalah

jawab

Rotasi [O, π/2] = [0, 90]

[tex]T1\,= \left[\begin{array}{ccc}cos 90&- sin 90\\sin 90&cos 90\end{array}\right] = \left[\begin{array}{ccc} 0 &-1\\1&0\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] [/tex]

x' = - y → y = - x'
y' = x → x = y'

x - y + 1 = 0  → y' - (-x') + 1= 0
y' + x' + 1= 0
bayangannya  x + y + 1= 0