If a straight line through the point (1,1) meets x axis at A and y-axis at B then the locus of midpoint AB is

Line meet x-axis at A(x,0) and y- axis at B (y,0) and point p(1,1) is the midpoint . Apply midpoint theorem to find coordinate of A and B 

For A(X,0) 

                 1=X+0/2

                  X=2 and same as y=2 …

Then find slope from coordinate A(2,0) and B(0,2) 

Slope =-1

 Apply eqn, 

                  y-y1 = m( x-x1) 

We get X+y-2 =0 as the eqn of locus of midpoint of AB