How is point F on line r lying on plane P?

Question

I had a math quiz about geometry and got 71% mainly because I didn't know that a plane extends in all directions infinitely. One question I had in particular I still don't understand was how point F, on line r lied on plane P, because even though the plane extends infinitely in all directions, it's still 2D. (I think so)

Line r is intersecting through plane P, with point F at the top of line r. How is point F on plane P if plane P is not 3D? Sorry if this is confusing to read

Answer 1

This drawing shows PART of plane P. Plane P does extend in TWO dimensions (2D).

It also show a LINE SEGMENT of line r.

Line r intersects Plane P at point F, The location of point F can be expressed with 2D coordinates in Plane P or as a position (like on the number line) on line r.

Note that all of the other points on line r ARE NOT on Plane P (they require 3D coordinates).

Also, all of the other points on Plane P ARE NOT on line r, only point F.