Find the projectivity $f$ in $\Bbb P^2(\Bbb R)$ that maps:
· Line $r: X_0=X_1$ to line $r': X_0+X_1=0$
· Line $s: X_0+X_1+X_2=0$ to line $s': X_1+X_2=0$
· Point $P[1:2:1]$ to point $P'[1:0:0]$
My thoughts: To define a projectivity I need two sets of $n+2$ points in general position, where $n$ is the dimension of the projective space I'm working on, so in this case I need four points. Given one point and two lines I only have two points, $P$ and the point of intersection of the two lines. Any hints?