Question

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

Answer 1

Since $(x,y)$ is the mid-point,

By midpoint formula,

$x=\frac{3+k}{2}$

$y=\frac{4+7}{2}=\frac{11}{2}$

Again,

the above coordinates should satisfy this line, $2x+2y+1=0$

So, $2\times \frac{3+k}{2}+2\times \frac{11}{2}+1=0$

$3+k+11+1=0$

$3+k+12=0$

$k+15=0$

$k=-15$