Question

The points $(2,1)$ and $(-3,-4)$ are opposite vertices of a parallelogram. If the other two vertices lie on the line $x+9y+c=0$, then $c$ is

• A. 12
• B. 14
• C. 13
• D. 15

Answer 1

Answer: (B)

14

Answer 2

The given line also passes through the point of intersection of the diagonals of the parallelogram, which is the mid-point of $(2,1)$ and $(-3,-4)$The mid-point of the given two points is $\bigg(-\frac{1}{2},-\frac{3}{2}\bigg)$.
Substituting the point in the given equation $-\frac{1}{2}+9×-\frac{3}{2}+c=0⇒c=14$

So, the correct answer is (B): $14$