Question

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

Answer 1

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

$\Rightarrow 3+k=2x$ -------(1)

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

$y=\frac{11}{2}$ -----------(2)

given that, k passes through the line 2x+2y+1=0

[From (1)] and (2)]

$\Rightarrow 3+k+11+1=0$

$\Rightarrow k+15=0$

$\Rightarrow k=-15$