Let (x, y) be the old coordinates and (X, Y) be the new coordinates. Therefore
x = X cosθ - Y sin θ ...(1)
and y = X sinθ + Y cos θ ...(2)
Solving Eq. (1) , We get
-2 = X cos 30° - Y sin 30°
⇒ -2 = √3X - Y/2
⇒ √3X - y = -4
Solving Eq. (2), we get
4 = X sin30° + Y cos 30°
⇒ 4 = X + √3Y/2
⇒ X + √3Y = 8 ...(4)
Solving Eqs. (3) and (4), we get X = 2 - √3 and Y = 1 + 2√3 are the new coordinates of (-2, 4).