Coordinates of A is (1,1),Coordinates of B is (5,4).

There is a point P moving over the line y=2x+4. When the sum of |AP|+|PB| is minimum with respect to P, find the ratio of PB to PA?

My work:

I found the symmetric of B. y=2x+4 so slope will be -1/2.

y-4=-1/2(x-5)

y=-x/2+13/2

y=2x+4

We find P as(1,6)

I found PA and PB AS 5 and squareroot20.