Solution: Let the analytical formula of AB line be y=kx+b, and bring it into A (-3/2,0) B (0,3) to obtain:

-3/2k+b=0

b=3

The solution is k= 2 b=3.

The analytical formula of the straight line is y=2k+3.

OP=2OA=3, and the coordinate of point P is (-9/2,0) or (3,0).

s△ABP = 1/2xAPxOB = 1/2x3x 3 = 9/2