As we know that (x,y) is the mid-point
$x=(3+k)/2$ and $y=(4+7)/2=11/2$
Also it is given that the mid-point lies on the line $2x+2y+1=0$
$2[(3+k)/2]+2(11/2)+1=0$
$3+k+11+1=0$
Thus, $k=-15$
As we know that (x,y) is the mid-point
$x=(3+k)/2$ and $y=(4+7)/2=11/2$
Also it is given that the mid-point lies on the line $2x+2y+1=0$
$2[(3+k)/2]+2(11/2)+1=0$
$3+k+11+1=0$
Thus, $k=-15$