Question

 the equation of perpendicular bisector of a line segment AB is x-y+5=0 if a=(1,-2) then AB is

Answer 1

perpendicular bisector of AB is x-y+5=0 or y=x+5
its slope = 1
so slope of AB = -1
equation of line with slope -1 is y=-x+c

AB passes through (1,-2)
thus, -2=-1+c
⇒c = -1
Equation of AB : y=-x-1 or x+y+1=0
Intersection of both the lines is the mid point of AB.
x-y+5 = 0
x+y+1 = 0
solving, we the point of intersection as (-3,2)

let point B is (m,n)
(m+1)/2=-3 
⇒ m = -7
(n-2)/2=2
⇒ n = 6

Point B is (-7,6)