... M on this line. ByProblems 30.1 and 30.3 there exists a unique projective transformation of the given line toitself that maps points A, B, C into A′, B′, C′, respectively. Denote this ... ay − by. Dividing this equality by a − b we get x = y.30.4. Let the image of each of the three given points under one projective transformationcoincide with the image of this point under another ... = 0, ax2+ b = cx2+ d, cx3+ d = 0.Find b and d from the first and third equations and substitute the result into the third one;we geta(x2− x1) = c(x2− x3)wherefrom we find the solution:...