Question 390390
The area of any triangle having vertices (a,b), (c,d), (e,f) is given by the absolute value of 
{{{det((matrix(3,3, a,b,1,c,d,1, e,f, 1)))/2}}}.  Hence we want absolute value of 


{{{det((matrix(3,3, 1,-3,1,4,2,1, x,y, 1)))/2 }}} = 6 or , after evaluating and simplifying the determinant, 

|3y - 5x + 14| = 12.  This is equivalent to 2 linear equations, namely 

3y - 5x = -2, OR

3y - 5x = -26.

Any point with coordinates satisfying either equation would form with the other two points a triangle of area 6.