Grade: 9 How many planes contain each line and point?
There are three of important facts here that show you how to solve this problem. First, if you have three distinct points in 3space then there is a plane that contains these three points. Second, if the three points lie on a line then there are in fact infinitely many planes that contain the three points. For example if the three points are A, B and C in your diagram then there are infinitely many planes that contain the points. I have illustrated two such planes in pink in the diagrams below. The final point is that if the three points do not lie on a line then there is exactly one plane that contains the points. For example if the points are A, B and E then, in the diagram on the right above, the plane coloured pink is the only plane that contains the three points. I hope this helps,Harley
