hey

 

let the point A be t1 and point B be t2

 

so now the point C come out to be [ ( t1+t2) /2 , t1.t2 ]

 

The midpoint of AB can be easily calculated. So, we find the length od median .. and this gives t1 - t2 = sqrt(2).m

 

Now one can easily find the area in terms of m

 

cheers