IMO 1985 LL ITA47

Origin: ITA

Problem

Let F be the correspondence associating with every point P = (x, y) the point P ′ = (x′, y′) such that x′ = ax + b, y′ = ay + 2b. (1) Show that if a ̸= 1, all lines PP ′ are concurrent. Find the equation of the set of points corresponding to P = (1, 1) for b = a2. Show that the composition of two mappings of type (1) is of the same type.