find the equation of a straight line which is equidistant from the points(2,3) and (6,1) expressing it in the form ax+by=c where a,b and c are constants.

Answer 1

The line must be the perpendicular bisector of the segment between the two points.
Since the slope of that segment is (1-3)/(6-2) = -1/2, your line must have slope 2
The midpoint of the segment is (4,2), so using the point-slope form, your line is

y-3 = 2(x-2)

now just put that into the desired form.

Answer 2

not understood

Answer 3

Equidistant of course means that the line its perpendicular to the two lines given find the gradient first that is

Gradient=Dy/DX
1-3/6-4= -1/2
Because it is perpendicular
M1XM2 =-1
Gradient of perpendicular = 2
Equidistant now (6+2)/2. (3+1)/2
Then follow it to the end

Answer 4

Y=1/2x+2