Question

Four points A, B, C, and D are coplanar, but only two at a time are collinear. Suppose a line is drawn through each pair of points. How many lines can you draw?

Answer 1

What I would do is try drawing these four points using the given information and finding all the lines you can use to connect a pair of points.

Answer 2

We may consider the flat surface you draw it on a plane for the "coplanar" definition. Then, you need only make it so that no three points can be on the same line to satisfy the "collinear" definition.

Answer 3

that means we can only have it like this:

and not like these:

now you can see from the first drawing that you can draw a total of six lines using these four points if we suppose there could only be two points at a time.