1. In answering the following questions, you may use whichever presentation(s) of the real projective plane you like, as long as you get the job done. a. Suppose (P, l) and (Q, m) are both non-incident point-line pairs in the real projective plane. Show that there is a collineation a, not necessarily central, such that Pa = Q and la = m. [5] Recall from class that a projective plane is (P, 1)-transitive for a point P and line 1 if whenever X and Y are points collinear with P, but not equal to P or on l, there is a (P, 1)-central collineation a such that Xa =Y. b. Show that the real projective plane is (P, 1)-transitive for every non-incident point-line pair (P, 1). [5] 1. In answering the following questions, you may use whichever presentation(s) of the real projective plane you like, as long as you get the job done. a. Suppose (P, l) and (Q, m) are both non-incident point-line pairs in the real projective plane. Show that there is a collineation a, not necessarily central, such that Pa = Q and la = m. [5] Recall from class that a projective plane is (P, 1)-transitive for a point P and line 1 if whenever X and Y are points collinear with P, but not equal to P or on l, there is a (P, 1)-central collineation a such that Xa =Y. b. Show that the real projective plane is (P, 1)-transitive for every non-incident point-line pair (P, 1). [5]