Given two points A(-2,0) and B(0,4) ,then find the coordinate of point p lying on the line 2x-3y=9 so that the perimeter of ∆APB is least

GIVEN QUESTION CAN BE SOLVED USING A.M-G.M INEQUALITY FOR PERIMETER TO BE MINIMUM AP +BP SHOULD BE MINIMUM i.e AP=BP OR SIMPLY P LIES ON PERPENDICULAR BISECTOR OF AB AND LINE2x-3y=9 i.e DEDUCE THE EQN OF PERPENDICULAR BISECTOR OF AB AND CALCULATE ITS POINT OF INTERSECTION WITH THE GIVEN LINE.THAT WILL BE YOUR ANSWER.