Given two points a = (-2,0) and b =(0,4 ) the coordinate of a point M lying on the line 2x-3y=9 so that permeter of triangle amb is least , is

GIVEN QUESTION CAN BE SOLVED USING A.M-G.M INEQUALITY FOR PERIMETER TO BE MINIMUM AM +BM SHOULD BE MINIMUM i.e AM=BM OR SIMPLY M 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.