Point, Line, and Plane are concepts which are very different, yet all intertwine with each other. I have provided different photos that I have taken in the past that I think explain the concepts.
This is my first image in Shasta valley northern California. Here we see all three concepts working with each other. This most blunt part of the image is the 2 vertical lines represented in the middle by 2 plants. This emphasizes the middle but also allows a representation of distance. The next is the 2 horizontal panes attached in the center from multiple point to create a visible line. The are divided by the natural lines that are created by the mountains and hills. Lastly, the to vertical lines create 3 segments in the image and spacing.
Here is a second image I took on my travels to Venice, Italy. Here we see 2 visible planes, the sky, and lower ground/water. We see to visible lines that represent distance increase towards the middle right. Lastly, the gondolier can represent single point on to the plane that is the canal. You also see lines going vertical and parallel to each other in the buildings of the canal.
Here is the last image, which was taken in Naples, Italy at about 1 a.m.
This line does a great job showing lines with the front fence leading the eyes in to the deeper layer of the image which would be the plane in the back on which the mountain shadow rest.