If `A(2,-1)a n dB(6,5)` are two points, then find the ratio in which the foot of the perpendicular from `(4,1)` to `A B` divides it.

Explanation

Let `(AM)/(MB)=(lambda )/(1)`
Therefore, the coordinates of M are
`((6lambda+2)/(lambda+1),(5lambda-1)/(lambda+1))`
`thereforePMbot AB`
or `(((5lambda-1)/(lambda+1)-1)/((6lambda+2)/(lambda+1)-4)){(5-1(-1))/(6-2)}=-1`
or `((2lambda-1)/(lambda+1))(3/2)=-1`
or `6lambda-3=2-2lambda`
or `lambda=(5)/(8)`