An application can rotate the flag counterclockwise through 90°, by applying:
x' = x cos 90 - y sin 90
y' = x sin 90 + y cos 90
Because cos 90 = 0 and sin 90 = 1, these equations become:
x' = - y
y' = x
The original five points are transformed: (0,0) ─ (0,0)
(0,4) ─ (-4,0)
(0,6) ─ (-6,0)
(2,4) ─ (-4,2)
(2,6) ─ (-6,2)
The following figure shows the effect of rotating the flag 90°.
Rotation Counterclockwise through 90°