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The place where two points meet is known as an intersection in math.
A two-dimensional surface on which points are plotted and located by their x and y coordinates
Six: top, bottom, two ends and two sides.
If the two lines are actually "on top of each other", they can have infinitely many points in common. If they are parallel, they have no points in common. If they are perpendicular, they have one point in common.
Yes, on a plane surface (a flat sheet of paper, for example).