Let  A7,5 and B1,2 are any two points. The ratio in which the foot of the perpendicular from  P2,3 to the line AB  divides it is

The slope of AB is m=2−51−7=12 The equation of the line perpendicular to AB and passing through the point P(2,3)iy−3=−2x−2y−3=−2x+42x+y−7=0 The ratio of the line segment joining two points A,B divided by the line L=0 is −LALB Hence, the ratio of line segment joining points A(7,5) and B(1,2) is divided by the line 2x+y−7=0 is −LALs=−2(7)+5−72(1)+2−7=123=4 Therefore, the ratio is 4:1