Intersection of line and plane

Question

I'm trying to figure out a problem in perspective geometry. Given the line from the origin to the point $P(x,y,z)$ at some point in space it casts a picture of a point when intersecting the plane $y=1$ given by $P'(x',1,z')$. I am then given a list of points and asked which pairs of points cast the same image on the plane. I have no idea where to start, how can I figure this out?

Answer 1

For each point $P=(x,y,z)$ on the list for which $y \neq 0,$ calculate (and store, with some indication of which point on the list it came from) the point $P'=(x/y,y/y,z/y).$ All points with the same $P'$ come from points on original list that cast the same image. Points for which $y=0$ on the original list will not cast any image on the plane.