Let S be a square region of side length 2. Show that among any 9 points in the square, there are 3 which form a triangle of area $\displaystyle \leq{\frac{1}{2}$.

I subdivided S into 8 triangles of equal area, $\displaystyle \frac{1}{2}$.

Now I divide into 2 cases

Case A: Where 3 points are in one triangle.

Then the area of said triangle $\displaystyle \leq{\frac{1}{2}$.

Case B: A max of 2 points are in any triangle

I'm having trouble with this case. Help please?