Solution: According to the two-point formula, the analytical formula of straight line AB can be obtained:

(y-5)/( 1-5)=(x- 1)/(6- 1)

Ordered: y=(-4/5)x+(29/5)

The abscissa of point O in line AB is: 1+(6- 1)/2=7/2.

Substitute x=7/2 into y=(-4/5)x+(29/5) to get y=3.

So the coordinate of the midpoint O of AB is O (7/2,3).

Because the product of slopes of two vertical lines is equal to-1.

So the slope of the straight line can be 5/4, so the analytical formula of the straight line can be set as: y = (5/4) x+b.

Because O (7/2,3) is also on a straight line, so

3=(5/4)*(7/2)+b

Solution: b=-1 1/8.

Therefore, the analytical formula of the median vertical line is: y=(5/4)x-( 1 1/8).