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Show that the lines PP' are concurrent

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September 13, 2010
geometry proposedgeometry

Problem Statement

Let FF be the correspondence associating with every point P=(x,y)P = (x, y) the point P′=(x′,y′)P' = (x', y') such that x′=ax+b,y′=ay+2b.(1) x'= ax + b,\qquad y'= ay + 2b. \qquad (1) Show that if a≠1a \neq 1, all lines PP′PP' are concurrent. Find the equation of the set of points corresponding to P=(1,1)P = (1, 1) for b=a2b = a^2. Show that the composition of two mappings of type (1)(1) is of the same type.
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