Let S be the set of points (a, b) in the coordinate plane, where each

The points should tell you that you are looking at a square with coordinates (-1,-1), (-1,1), (1,1) and (1,-1). The centre of the square and midpoint of each side are other points..
So, in total we have 9 points. But, the centre will always be part of 3 points.

So we are left with 8 points, and we have to choose 2 out of it, so 8C2=8*7/2=28.
Now, the sides of the square consists of 3 points. We have counted each side thrice, so 4*2 are repeated. Thus, 28-8=20.
For example.. side containing points A(-1,-1), B(-1,0) and C(-1,1).. The line is only one but we have calculated it thrice in our calculations. AB, BC and AC, whereas it is just on eline AC.

B