Question

If the mid-point of the line joining $(3,4)$ and $(p,7)$ is $(x,y)$ and $2x+2y+1=0$, then $p$ is equal to

• A. $15$
• B. $-\frac{17}{2}$
• C. $-15$
• D. $\frac{17}{2}$

Answer 1

Answer: (C)

$-15$

Since $(x,y)$ is the mid-point of the line joining $(3,4)$ and $(p,7)$
$\therefore x=\frac{3+p}{2},y=\frac{4+7}{2}$
$\Rightarrow 2x=3+p,2y=11$
Since $2x+2y+1=0$
$\therefore 3+p+11+1=0$

$\Rightarrow p=-15$