Projective Geometry etbadrilaternl and u a point un A8x M be

etbadrilaternl and u a point un (A.8:x M be inturthon of the lne(8, C and

Solution

Let E = AB?CD, F = AD ?BC.

Consider the sequence of perspectivities ABEM1 =? D FBCM2 =? A DECM3 =? B DAFM4 =? C EABM5. (eq.) According to the conditions given in the problem this sequence of perspectivites has two be applied three more times to arrive to the point M13. Notice that the given sequence of perspectivities maps A to E, E to B, and B to A. Clearly if we apply (eq.) three times the points A, B, and E will be fixed while M1 will be mapped to M13. Thus M1 = M13