if the coordinates of the mid-point of the line-segment joining the points(2,1) and (1,-3) is (x,y) then the relation between x and y can be best described by i)3x +2y=5 ii) 6x +y=8 iii) 5x-2y=4 iv)2x-5y=4

The midpoint joining the points given will be
((2+1)/2,(1-3)/2)=(3/2,-1). Try putting these points in the give line equations. Only (ii) satisfies it.

Given that the coordinates of the mid-point of the line segment joining the points(2,1) and (1,-3) are (x, y)
So, (x, y) = ((2+1)/2,(1-3)/2)
(x, y) = (3/2, -1)
Any equation that passes through (3/2, -1) satisfies the equation.
Among the given options only 6x + y = 8 satisfies. Hence, Option B.