Prove that the perpendicular drawn from the point (4, 1) on the line joining the points (2, −1) and (6, 5) divides it in the ratio 5 : 8

Dear Student. You can easily find out the equation of perpendicular line (point slope form) and the line joining the two given points(two point form) from the given information. Then solve then two equation to get the intersecting points. Then use the section formula to prove it. Thanks.