If the mid-point of the line joining $(3,4)$ and $(k,7)$ is (x, y) and $2x+2y+1=0$ then find the value of k.

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, $k=-15$